A method for reducing multipath effect of take-off and landing guidance radar based on adaptive off-axis tracking

Abstract

The present invention provides a method for reducing the multipath effect of a take-off and landing guidance radar based on adaptive off-axis tracking, comprising: the take-off and landing guidance radar transmits a signal, and after receiving the signal, transmits the signal in the direction of the radar; the radar simultaneously receives the direct signal and the multipath signal, separates and establishes a temporal and spatial feature database of the multipath signal; when the impact of the signal on the angular error exceeds a dynamic threshold, the off-axis tracking mode is activated; the optimal off-axis angle is dynamically calculated, the antenna elevation angle is locked, and closed-loop tracking of the azimuth is performed; joint analysis is performed to identify and eliminate false targets in real time; random angle errors are intelligently suppressed; and phase and amplitude compensation is performed on the received signal by constructing a real-time multipath propagation model. The present invention has excellent real-time performance and engineering feasibility, and can meet the strict requirements of aircraft precision approach guidance. It has good scalability and adaptability, and provides reliable technical support for ensuring the safe take-off and landing of aircraft in adverse weather and complex environments.

Description

Technical Field

[0001] The present invention relates to the field of radar engineering and avionics technology, and in particular to a method for reducing multipath effects of a take-off and landing guidance radar based on adaptive off-axis tracking. Background Art

[0002] Takeoff and landing guidance radars are critical equipment for ensuring safe takeoff and landing of aircraft, primarily used to accurately track and guide aircraft during the approach and landing phases. However, in practical applications, radars are severely impacted by multipath when tracking targets at low elevation angles. Multipath refers to the phenomenon in which electromagnetic waves emitted by radars, in addition to directly reaching the target, are also reflected by the ground, buildings, and other objects before reaching the target. These reflected signals superimpose on the direct signal, causing changes in the amplitude and phase of the received signal, which in turn leads to angle measurement errors.

[0003] During the aircraft's approach and landing phase, the target's altitude gradually decreases, and the elevation angle continuously decreases, making the impact of multipath increasingly severe. When the aircraft is close to the runway and at a low altitude, the intensity of the ground-reflected signal may approach or even exceed the direct signal, causing radar tracking instability, increasing angle measurement errors, and even generating false targets, seriously compromising flight safety. Statistics show that at elevation angles less than 1°, multipath can cause angle measurement errors exceeding 0.2°, which is unacceptable for precision approach guidance.

[0004] Existing multipath suppression technologies mainly include: first, the use of low sidelobe antenna technology to reduce the reception of ground-reflected signals by reducing the antenna sidelobe level, but this method has limited effect at extremely low elevation angles; second, the use of multi-frequency point measurement to identify and suppress multipath signals, but this increases system complexity and cost; third, the use of polarization diversity technology to suppress multipath signals by utilizing the difference in polarization characteristics between direct signals and reflected signals, but this is not effective under certain ground conditions; fourth, the use of traditional off-axis tracking technology to deviate the antenna main lobe from the target by a certain angle to reduce the impact of multipath, but the off-axis angle usually adopts a fixed value or a simple linear relationship and lacks adaptive capabilities.

[0005] Furthermore, existing technologies often rely on passive multipath suppression, lacking the ability to proactively predict and compensate for it. Traditional signal processing methods, primarily based on statistical models, struggle to adapt to the complex and ever-changing airport environment. With the ever-changing environment surrounding airports, and during wartime, there's no prior knowledge of the multipath effects of newly seized runways, and the characteristics of multipath also change dynamically, making existing static processing methods ill-suited to these changes.

[0006] Therefore, a new method is urgently needed that can predict multipath effects in real time, adaptively adjust tracking strategies, intelligently identify false targets, and accurately compensate for them. This method can improve the tracking accuracy and reliability of takeoff and landing guidance radars at low elevation angles and ensure the safe takeoff and landing of aircraft. Especially in adverse weather conditions, the accuracy of radar guidance is directly related to flight safety, making the solution to the multipath effect even more urgent and important. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention proposes a method for reducing the multipath effect of takeoff and landing guidance radars based on adaptive off-axis tracking. This method exhibits excellent real-time performance and engineering feasibility, with an environmental anomaly detection response time of less than 5 seconds and a system recovery time of less than 30 seconds, meeting the stringent requirements for precision approach guidance for aircraft. By establishing a long-term learning mechanism and an environmentally adaptive update strategy, system performance continuously improves over time, demonstrating excellent scalability and adaptability, providing reliable technical support for ensuring safe takeoff and landing of aircraft in adverse weather and complex environments.

[0008] To achieve the above object, the present invention proposes a method for reducing the multipath effect of a take-off and landing guidance radar based on adaptive off-axis tracking, comprising the following steps:

[0009] Step S1: The takeoff and landing guidance radar transmits a multi-frequency interrogation signal to the airborne transponder. After receiving the interrogation signal, the airborne transponder transmits a response signal in the direction of the radar.

[0010] Step S2: The radar simultaneously receives the direct signal and the multipath signal generated by the reflection of the ground or obstacles, separates the direct signal and the multipath signal through multi-dimensional signal feature extraction technology, and establishes a temporal and spatial feature database of the multipath signal;

[0011] Step S3: Predicting the evolution trend of the multipath effect in real time based on a machine learning algorithm. When the impact of the predicted multipath signal on the angular error exceeds a dynamic threshold, the adaptive off-axis tracking mode is activated in advance.

[0012] Step S4: In the off-axis tracking mode, the optimal off-axis angle is dynamically calculated based on the target height, distance, descent speed and environmental multipath characteristics, and the antenna is locked at this angle while continuing the closed-loop tracking of the azimuth.

[0013] Step S5: Establish a multipath signal false target recognition model, and through time domain-frequency domain-spatial domain joint analysis, identify and eliminate multipath false targets in real time, retaining the real target information;

[0014] Step S6: Adopting an angle error estimation method that integrates adaptive Kalman filtering and deep learning to intelligently suppress the angle random error caused by multipath and achieve predictive tracking of the target motion trajectory;

[0015] Step S7: When it is detected that the target has entered the critical landing phase, the multipath effect compensation mode is started. By building a real-time multipath propagation model, the phase and amplitude of the received signal are compensated to improve the tracking accuracy.

[0016] Furthermore, the multi-dimensional signal feature extraction technology includes:

[0017] Step 2.1: Time domain feature extraction: Perform high-speed sampling on the received direct and multipath signals. Calculate the time delay difference between the multipath and direct signals using a cross-correlation algorithm. Extract the signal envelope using a Hilbert transform, calculate the pulse width change rate, and analyze the signal temporal correlation using a sliding window technique.

[0018] Step 2.2: Frequency domain feature extraction: Use N1-point FFT transform to perform spectrum analysis, extract characteristic parameters such as Doppler frequency shift and spectrum centroid, calculate power spectrum density, and analyze spectrum broadening characteristics, where N1 is the number of FFT transform points, which is 1024.

[0019] Step 2.3: Spatial feature extraction: Based on the N2-element uniform linear array, a spatial covariance matrix is ​​constructed. The signal and noise subspaces are obtained through eigenvalue decomposition. The MUSIC algorithm is used for high-precision arrival angle estimation. The root MUSIC algorithm and parabolic interpolation are combined to improve the angle estimation accuracy. Where N2 is the number of antenna elements, which is 8.

[0020] Step 2.4: Polarization feature extraction: Measure the horizontal H and vertical V polarization components simultaneously, calculate the complex polarization ratio, extract characteristic parameters such as polarization ellipticity and polarization angle, and analyze the change in polarization state;

[0021] Step 2.5: Feature vector construction: The extracted multidimensional features are combined into a 6-dimensional feature vector F = [Δt, ΔT / T0, fd, θ, φ, ε]. The feature vector is reduced to 4 dimensions through principal component analysis, retaining 95% of the variance information to form the final multipath feature descriptor, where:

[0022] Δt: multipath delay difference, unit: s

[0023] ΔT: Pulse width change, unit s

[0024] T0: standard pulse width, unit: s

[0025] fd: Doppler frequency shift, unit Hz

[0026] θ: signal arrival angle, unit: °

[0027] φ: azimuth, unit: °

[0028] ε: polarization ellipticity, dimensionless.

[0029] Furthermore, the multipath effect prediction based on machine learning includes the following detailed steps:

[0030] Step 3.1: Data collection and preprocessing: Establish a long-term data collection mechanism to collect multipath characteristic data under different environmental conditions, perform data cleaning and remove outliers, normalize the input data, and divide the training set, validation set, and test set into a ratio of 7:2:1.

[0031] Step 3.2: Data augmentation is performed by adding Gaussian white noise with a signal-to-noise ratio (SNR1) of 20 dB. Random jitter is performed in the time dimension, and new samples are generated by linear interpolation between adjacent samples to expand the training dataset. SNR1 is the baseline signal-to-noise ratio for data augmentation.

[0032] Step 3.3: Deep neural network construction, design a three-layer fully connected network architecture, with N3 nodes in the input layer, N4 nodes in the first hidden layer, N5 nodes in the second hidden layer, and N6 nodes in the output layer. Add batch normalization and dropout layers to each layer, and set the dropout probability p1, where:

[0033] N3: Number of input layer nodes, value is 64

[0034] N4: The number of nodes in the first hidden layer, the value is 128

[0035] N5: The number of nodes in the second hidden layer, the value is 64

[0036] N6: The number of output layer nodes, which is 3, corresponds to the three prediction targets of Mp, Δφ, and Δt.

[0037] p1: dropout probability, value 0.3

[0038] Mp: multipath strength, dimensionless

[0039] Δφ: multipath phase difference, unit rad

[0040] Δt: multipath delay difference, unit is s;

[0041] Step 3.4: Design an LSTM temporal network. Build a long short-term memory network to learn the temporal variation of the multipath effect. Set the input sequence length to 10 time steps, the hidden layer to 50 units, and integrate the attention mechanism to identify key moments to achieve temporal modeling of the multipath effect.

[0042] Step 3.5: Model training and optimization. Use the improved loss function L = MSE + λ1∑wi² and the Adam optimizer for model training. Set the early stopping mechanism to prevent overfitting and use gradient clipping to prevent gradient explosion. Where λ1 is the L2 regularization coefficient, with a value of 0.001, and wi is the network weight parameter.

[0043] Step 3.6: Multi-model fusion prediction, weighted fusion of DNN and LSTM network outputs, the prediction formula is Mp pred (t+k) = α1·DNN out + α2 LSTM out , to achieve forward-looking prediction of multipath strength, where:

[0044] Mp pred (t+k): multipath strength predicted in k steps

[0045] k: prediction step length, ranging from 3 to 5 scan cycles

[0046] α1: DNN network weight, value is 0.6

[0047] α2: LSTM network weight, value is 0.4

[0048] DNN out : Deep neural network output

[0049] LSTM out : LSTM network output;

[0050] Step 3.7: Dynamic threshold calculation: Calculate the dynamic trigger threshold based on historical statistical data and current change trends. The threshold formula is: , to achieve an adaptive early warning mechanism, including:

[0051] : Dynamic threshold at time t

[0052] : Historical multipath intensity average

[0053] : Historical multipath intensity standard deviation

[0054] k1: statistical weight coefficient, value is 2.5

[0055] k2: Change rate weight coefficient, value is 0.15

[0056] : Multipath intensity change rate.

[0057] Furthermore, the intelligent elevation angle locking strategy includes the following implementation steps:

[0058] Step 4.1: Geometric relationship establishment: Based on the radar height hr, target height ht, and horizontal distance d, a three-dimensional geometric model of the radar-target-ground is established. The direct angle and reflection angle are calculated, and the mirror target position is determined, providing a geometric basis for subsequent optimization.

[0059] Step 4.2: Calculate the reflection coefficient. Based on the ground material type and electromagnetic properties, use the Fresnel formula to calculate the reflection coefficient at different incident angles, taking into account the impact of environmental factors such as ground humidity and roughness on the reflection characteristics.

[0060] Step 4.3: Design the optimal angle objective function and establish the comprehensive optimization objective function F opt (θ x ) = w1·G mp (θ x )+ w2·G track (θ x ), balancing the multipath suppression effect and tracking performance loss, where:

[0061] F opt (θ x ): Angle θ x Comprehensive optimization function under

[0062] θ x : candidate off-axis angle, unit: °

[0063] w1: multipath suppression weight, value is 0.7

[0064] w2: tracking performance weight, value 0.3

[0065] G mp (θ x ): Multipath suppression gain function

[0066] G track (θ x ): Tracking performance function;

[0067] Step 4.4: Numerical optimization solution: Use the golden section method to find the optimal off-axis angle in the search interval [0°, 2°]. Set the convergence accuracy to 0.1° and the maximum number of iterations to 100 to ensure the convergence and real-time performance of the algorithm.

[0068] Step 4.5: Dynamic constraint control, set the angular velocity constraint |dθ / dt| ≤ ω max and the angle range constraint θ ∈ [θ min , θ max ], where ω max is the maximum angular velocity limit, which is 0.5° / s, θ min The minimum off-axis angle is 0.2°, θ maxThe maximum off-axis angle is 1.8°;

[0069] Step 4.6: Smoothing filtering: Use a 3rd-order Butterworth low-pass filter to smooth the angle command, with the cutoff frequency set to 0.1Hz to prevent antenna system oscillation and ensure the stability of angle changes;

[0070] Step 4.7: Adaptive parameter adjustment, real-time monitoring of environmental changes, when the environmental mutation index ECI = |Mp cur -Mp pred | / σ pred >Th env , triggers a rapid recalculation of parameters, where:

[0071] ECI: Environmental Change Index

[0072] Mp cur : The currently measured multipath strength

[0073] Mp pred : Predicted multipath strength

[0074] σ pred : Standard deviation of prediction error

[0075] Th env : Environmental change threshold, the value is 2.5.

[0076] Furthermore, the multipath false target recognition model includes the following processing steps:

[0077] Step 5.1: Coherence detection and analysis: calculate the coherence time and coherence bandwidth of the received signal, analyze the signal correlation characteristics through the cross-correlation function, calculate the coherence coefficient, and mark it as a suspicious target when the coherence coefficient is lower than the set threshold;

[0078] Step 5.2: Trajectory consistency verification: Build a four-dimensional state space Kalman filter that includes target position and velocity information. Analyze trajectory consistency through innovation test. When the innovation covariance exceeds the statistical threshold, mark it as a trajectory anomaly.

[0079] Step 5.3: RCS characteristic analysis: establish a target radar cross-section database, measure the target RCS value in real time, compare and analyze it with the theoretical model, calculate the anomaly index, and identify RCS anomalies caused by multipath effects;

[0080] Step 5.4: Multi-frame data association: Set a time window for multi-frame data association analysis, calculate the probability of the target's presence between consecutive frames, analyze the continuity and consistency of the target's motion, and eliminate intermittent false targets;

[0081] Step 5.5: Multi-dimensional confidence fusion, weighted fusion of the results of the four detection methods, the fusion formula is C total = w1·C coh + w2·C traj + w3·C rcs + w4·C prob , establish a comprehensive sentencing mechanism, which includes:

[0082] C total : Comprehensive confidence, value range [0,1]

[0083] C coh : Coherence confidence

[0084] C traj : Trajectory consistency confidence

[0085] C rcs : RCS characteristic confidence

[0086] C prob : Existence probability confidence

[0087] w1, w2, w3, w4: fusion weights, 0.3, 0.3, 0.2, 0.2 respectively;

[0088] Step 5.6: Adaptive threshold adjustment: dynamically adjust the decision threshold according to the multipath strength and signal-to-noise ratio level of the current environment. The threshold calculation formula is Th adapt = Th base + k3·Mp level + k4·SNR factor ,in:

[0089] Th adapt : Adaptive decision threshold

[0090] Th base : Basic threshold, value is 0.75

[0091] Mp level : Current multipath strength level

[0092] SNR factor : Signal-to-noise ratio impact factor

[0093] k3: multipath strength adjustment coefficient, value is -0.1

[0094] k4: Signal-to-noise ratio adjustment coefficient, set to 0.05.

[0095] Furthermore, the adaptive Kalman filter and deep learning fusion method includes the following implementation steps:

[0096] Step 6.1: Improve the state equation design and introduce the multipath error compensation term based on the traditional Kalman filter state equation. The state equation is X(k x +1) = [I + ΔT s ·A + Δm comp (k x )]X(k x ) + ΓU(k x ) + W(k x ),in:

[0097] X(k x ): state vector at time kx, including position and velocity information;

[0098] I: identity matrix;

[0099] ΔT s : Sampling interval, value is 0.1s;

[0100] A: system state transfer matrix;

[0101] Δm comp (k x ): Multipath error compensation matrix, estimated in real time by neural network;

[0102] Γ: control input matrix;

[0103] U(k x ): control input vector;

[0104] W(k x ): process noise vector;

[0105] Step 6.2: Neural network noise estimation: Two independent three-layer neural networks are designed to estimate the process noise and observation noise covariance matrices respectively. The network inputs include multipath intensity, signal-to-noise ratio, and target motion parameters to achieve adaptive modeling of noise characteristics.

[0106] Step 6.3: Reinforcement learning gain optimization: Use the Q-learning algorithm to optimize the Kalman gain parameters. The state space includes multipath strength, signal-to-noise ratio, and prediction error. The action space is the gain adjustment. The reward function guides the parameter optimization direction.

[0107] Step 6.4: Multi-model structure establishment, establish three motion models: cruise (CV), acceleration (CA), and turning (CT), calculate the probability of each model through the likelihood function, and the model probability update formula is μ i (k y ) = L i (k y )μ i (k y -1) / ∑j Lj (k y )μ j (k y -1), where:

[0108] μ i (k y ): The i-th model in k y Probability of moment

[0109] L i (k y ): likelihood function of the i-th model

[0110] μ i (k y -1): The i-th model is in k y -1 moment probability;

[0111] Step 6.5: Adaptive parameter adjustment, dynamically adjust the learning rate and forgetting factor according to the stability of the environment. The learning rate formula is α lr (k z ) = α0 / (1+β·k z ), where α0 is the initial learning rate with a value of 0.01, β is the decay coefficient with a value of 0.001, and k z is the number of iterations;

[0112] Step 6.6: Filter fusion output, fuse the multi-model filtering results according to probability weighting, and output the final state estimation and covariance to achieve accurate tracking of target motion in multipath environment.

[0113] Furthermore, the multipath effect compensation mode includes the following technical steps:

[0114] Step 7.1: 3D environmental modeling: Integrate terrain data, building information, and material properties to create a high-precision 3D environmental model with a grid resolution of 5m×5m, taking into account propagation characteristics such as atmospheric refraction and absorption.

[0115] Step 7.2: Ray tracing calculation, using the geometric optics approximation method, calculates the multipath propagation path of the electromagnetic wave, considering up to three reflections, and calculates the reflection and transmission coefficients of each interface according to the Fresnel formula;

[0116] Step 7.3: Adaptive beamforming, calculate the optimal weight vector based on the desired signal direction and interference distribution , suppressing multipath interference in the spatial domain, where:

[0117] w beam : beamforming weight vector

[0118] R cov : Received signal covariance matrix

[0119] s steer : expected signal steering vector;

[0120] Step 7.4: Time domain equalization processing uses a 32-order FIR adaptive equalizer and updates the filter coefficients in real time through the LMS algorithm to compensate for inter-symbol interference caused by multipath and improve signal quality.

[0121] Step 7.5: Compensation effect evaluation: calculate the signal-to-interference-noise ratio improvement and tracking error reduction rate in real time. The evaluation formula is:

[0122] ;

[0123] Signal-to-Interference-Noise Ratio Improvement Evaluation

[0124] : Tracking error reduction rate evaluation where:

[0125] SINR imp : Signal-to-interference-and-noise ratio improvement, unit: dB, target value ≥ 6dB

[0126] P after , P before : Signal power before and after compensation

[0127] N after , N before : Noise power before and after compensation

[0128] ER track : Tracking error reduction rate, dimensionless, target value ≥ 0.4

[0129] σ before , σ after : standard deviation of tracking error before and after compensation;

[0130] Step 7.6: Dynamic parameter adjustment: adjust the algorithm parameters in real time according to the compensation effect. When the compensation effect is lower than expected, automatically switch the compensation strategy or adjust the parameter settings.

[0131] Furthermore, the method also includes a multi-radar cooperative anti-multipath technology:

[0132] Step 8.1: Multi-radar network configuration, the main radar and N9 = 2-3 auxiliary radars form a network, the distance between radars D = 200-500m, ensure that the baseline length B meets , where ρ4 is the required resolution, h is the target height, is the radar signal wavelength, The distance between the radar and the target;

[0133] Step 8.2: Data fusion algorithm, using weighted least squares method, weight , where σ i is the standard deviation of the measurement error of the i-th radar; the fusion estimate x̂ = Σ(w i x i ) / Σw i , x i is the measurement value of the i-th radar, with covariance P = 1 / Σw i ;

[0134] Step 8.3: Interference coordination mechanism: Time division multiplexing (TDM). Each radar transmits at a time interval staggered by Δt3 = 2R6 / c + τ1, where τ1 = 10 μs is the guard time, R6 is the maximum distance between the radar and the target, and c is the speed of light. Frequency division multiplexing (FDM) uses a frequency interval Δf2 ≥ 2 / T2, where T2 is the pulse width.

[0135] Step 8.4: Dominance Switching Algorithm, Define Radar Quality Factor , where SNR i is the signal-to-noise ratio, σ θi is the angle error, M pi is the multipath strength; when Q j >1.5Q i Switch the dominant radar (Q i When is the quality factor of the current dominant radar, the dominance is switched to radar ( j ). This mechanism ensures that the radar with the best performance is always selected as the dominant radar);

[0136] Step 8.5: Collaborative Gain Evaluation, Multi-radar Positioning Accuracy Improvement Factor , where N 10 is the number of radars, Δθ1 is the angle between radars, and the target G ≥ 1.5.

[0137] Furthermore, the method also includes a multipath suppression technology based on target scattering characteristics:

[0138] Step 9.1: Establish an RCS database. Collect and build a radar cross-section database for 20 typical civil airliners, including the A320, B737, and C919. For each aircraft type, samples are collected at 1° intervals within a 360° azimuth and 40° elevation range. The data covers different frequencies and polarization modes, forming a complete target signature database.

[0139] Step 9.2: Real-time RCS measurement: Use single-pulse angle measurement technology to measure the target's RCS in real time. Calculate the scattering cross-section using the radar equation, perform multiple pulse accumulation to improve measurement accuracy, and correct for environmental factors such as atmospheric attenuation and precipitation attenuation to ensure measurement accuracy of ±1dB.

[0140] Step 9.3: RCS model matching: Based on the target recognition results, the theoretical RCS model of the corresponding aircraft model is extracted from the database. Taking into account the target's current flight attitude, distance, and angle, the expected RCS theoretical value is calculated to provide a benchmark for anomaly detection.

[0141] Step 9.4: Scattering anomaly detection, define the RCS anomaly index AI = |σ m - σ e | / σ e , set the hierarchical decision threshold, implement anomaly detection and classification, where:

[0142] AI: RCS Anomaly Index

[0143] σ m : Measured RCS value, unit: m²

[0144] σ e : Expected RCS value, unit: m²

[0145] Decision rules: AI>0.4 is considered a suspicious target, and AI>0.7 is considered an abnormal target;

[0146] Step 9.5: Attitude angle compensation, considering the impact of the target flight attitude on RCS, use the attitude compensation formula σ e =σ model (θ,φ)·cos(α), where α is the attitude deviation angle, corrects the expected RCS value to improve the accuracy of anomaly detection;

[0147] Step 9.6: Polarization characteristic analysis, while measuring the horizontal polarization RCS (σ HH ) and vertical polarization RCS(σ VV ), calculate the polarization ratio PR = σ VV / σ HH , analyze the change of polarization characteristics, the normal range PR ∈ [0.1, 3.5], when it exceeds the range, it is determined to be affected by multipath;

[0148] Step 9.7: Angular glint detection, analyze the temporal variation characteristics of RCS through continuous measurement, and calculate the standard deviation σ of the RCS measurement sequence r and mean μ r , define the angular scintillation index AS = σ r / μ r ,in:

[0149] AS: Angular scintillation index, dimensionless

[0150] σ r : RCS standard deviation, unit m²

[0151] μ r: RCS mean, unit: m²

[0152] Judgment criteria: normal target AS < 0.3, multipath affected AS > 0.6;

[0153] Step 9.8: Comprehensive characteristic evaluation: Comprehensively evaluate the results of RCS anomaly detection, polarization characteristic analysis, and angular glint detection, establish a multi-dimensional target authenticity verification mechanism, and improve the reliability of false target identification.

[0154] Furthermore, the method also includes an environment adaptive learning mechanism, including the following technical steps:

[0155] Step 10.1: Construct an airport environmental database. This database integrates multi-source data to create a comprehensive environmental database, including terrain elevation data (accuracy ±0.5m), 3D building models (accuracy ±1m), and ground material distribution information, including electromagnetic properties of 15 typical materials, including concrete, asphalt, metal, and vegetation.

[0156] Step 10.2: Model the material reflection characteristics and establish a database of complex dielectric constants of different ground materials, including concrete (ρ c =0.3-0.5), asphalt (ρ a =0.1-0.2), metal (ρ m =0.8-0.9), vegetation (ρ v =0.05-0.1) etc., where:

[0157] ρ c : Concrete reflection coefficient

[0158] ρ a : Asphalt reflection coefficient

[0159] ρ m : Metal reflection coefficient

[0160] ρ v : vegetation reflectance;

[0161] Step 10.3: Pre-calculate the multipath distribution. For each runway direction of the airport (e.g., 09 / 27, 15 / 33), pre-calculate the multipath intensity distribution map M within the 450° azimuth × 40° elevation grid. n (θ, φ), stored in a 2D lookup table format, to establish a fast query mechanism;

[0162] Step 10.4: Seasonal data update: Establish a hierarchical dynamic update strategy, with static data (topography and buildings) updated annually, semi-static data (vegetation changes) updated quarterly, and dynamic data (meteorological parameters) updated in real time to ensure the accuracy of the environmental model;

[0163] Step 10.5: Adaptive modeling of environmental parameters: Establish a model of the impact of environmental parameters on multipath effects, including:

[0164] Temperature affects the refractive index:

[0165] Humidity affects reflection coefficient: ρ h (H) = ρ dry + 0.1×(H / 100)

[0166] Wind speed affects scattering characteristics: σ s = σ0(1 + 0.02V) where:

[0167] n: atmospheric refractive index,

[0168] P: atmospheric pressure, unit Pa

[0169] T: absolute temperature, unit K

[0170] e: water vapor pressure, unit Pa

[0171] ρ h (H): Humidity-related reflectance

[0172] ρ dry : Dry condition reflection coefficient

[0173] H: relative humidity, unit %

[0174] σ s : scattering cross-sectional area, unit: m²

[0175] σ0: reference scattering cross-sectional area, unit: m²

[0176] V: wind speed, unit: m / s;

[0177] Step 10.6: Model parameter online optimization, using the least squares method to update the environmental model parameters in real time, the objective function J = Σ(y real -y model )², set the parameter variation constraint |Δp| ​​≤ 0.1p, where:

[0178] J: Optimize objective function

[0179] y real : Actual observed value

[0180] y model : Model predicted value

[0181] Δp: parameter change

[0182] p: model parameters

[0183] Convergence criterion: |∇J|<10^(-6) or number of iterations>1000;

[0184] Step 10.7: Abnormal event detection and response, establish an environmental anomaly monitoring mechanism, and define the environmental anomaly index EAI = |M cur -M hist | / σ hist When EAI>3, the abnormal response mode is triggered, where:

[0185] EAI: Environmental Anomaly Index

[0186] M cur : Current multipath strength measurement value

[0187] M hist : Historical multipath intensity average

[0188] σ hist : Standard deviation of historical data;

[0189] Step 10.8: Rapid Response and Recovery: Develop a rapid response mechanism for abnormal situations, including parameter recalibration, rapid model retraining, and activation of backup strategies. The requirement is that the anomaly detection response time should be less than 5 seconds, the parameter adjustment time should be less than 30 seconds, and the system recovery time should be less than 30 seconds.

[0190] Step 10.9: Adaptive learning optimization: Establish a long-term learning mechanism to continuously optimize the environmental model and prediction algorithm through accumulated observation data, improve the system's adaptability to environmental changes and prediction accuracy, and achieve continuous improvement of system performance.

[0191] Compared with the prior art, the present invention has the following beneficial effects:

[0192] 1. This invention provides a method for reducing the multipath effect of takeoff and landing guidance radars based on adaptive off-axis tracking. By establishing an intelligent multipath suppression system that combines multidimensional signal feature extraction with machine learning prediction, this system achieves active prediction and adaptive suppression of multipath effects. Compared to traditional passive suppression methods, this solution can predict the evolution of multipath effects 3-5 scanning cycles in advance and dynamically adjust the off-axis tracking angle, reducing the angle measurement error from over 0.5° to under 0.1°, significantly improving tracking accuracy at low elevation angles.

[0193] 2. This invention provides a method for mitigating the multipath effects of takeoff and landing guidance radars based on adaptive off-axis tracking. By integrating a prediction model based on a deep neural network and an LSTM time series network, combined with real-time monitoring of environmental parameters, this method achieves adaptive learning for complex and changing airport environments. The system dynamically updates the multipath propagation model based on factors such as ground texture, meteorological conditions, and seasonal variations. Using an online optimization algorithm, it adjusts compensation parameters in real time, ensuring stable tracking performance across diverse environmental conditions.

[0194] 3. This invention provides a method for mitigating the multipath effects of takeoff and landing guidance radars based on adaptive off-axis tracking. Through multidimensional joint analysis across the time, frequency, spatial, and polarization domains, combined with target RCS characteristics and trajectory consistency verification, a comprehensive confidence assessment mechanism is established, achieving an accuracy rate exceeding 95% for false target identification. Furthermore, the fusion of adaptive Kalman filtering and deep learning enables the system to intelligently estimate and compensate for noise characteristics, further improving the stability and continuity of target tracking.

[0195] 4. This invention provides a method for reducing the multipath effects of takeoff and landing guidance radars based on adaptive off-axis tracking. By fusing data from two to three radars, positioning accuracy is increased by more than 1.5 times. When the primary radar is subject to severe multipath interference, it automatically switches to the radar with the best performance, ensuring system reliability. Furthermore, an anomaly detection mechanism based on target scattering characteristics can identify multipath effects from a physical perspective, further enhancing system robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0196] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0197] Figure 1 This is a schematic diagram of the process of the present invention

[0198] Figure 2 It is a schematic diagram of the geometric model of the multipath effect of the take-off and landing guidance radar;

[0199] Figure 3 It is a schematic diagram for comparing performance indicators; DETAILED DESCRIPTION

[0200] The technical solutions of the present invention will be more clearly and completely explained below through description of preferred embodiments of the present invention in conjunction with the accompanying drawings.

[0201] like Figure 1 As shown,

[0202] Step S1: The takeoff and landing guidance radar transmits a multi-frequency interrogation signal to the airborne transponder. After receiving the interrogation signal, the airborne transponder transmits a response signal in the direction of the radar.

[0203] Step S2: The radar simultaneously receives the direct signal and the multipath signal generated by the reflection of the ground or obstacles, separates the direct signal and the multipath signal through multi-dimensional signal feature extraction technology, and establishes a temporal and spatial feature database of the multipath signal;

[0204] Step S3: Predicting the evolution trend of the multipath effect in real time based on a machine learning algorithm. When the impact of the predicted multipath signal on the angular error exceeds a dynamic threshold, the adaptive off-axis tracking mode is activated in advance.

[0205] Step S4: In the off-axis tracking mode, the optimal off-axis angle is dynamically calculated based on the target height, distance, descent speed and environmental multipath characteristics, and the antenna is locked at this angle while continuing the closed-loop tracking of the azimuth.

[0206] Step S5: Establish a multipath signal false target recognition model, and through time domain-frequency domain-spatial domain joint analysis, identify and eliminate multipath false targets in real time, retaining the real target information;

[0207] Step S6: Adopting an angle error estimation method that integrates adaptive Kalman filtering and deep learning to intelligently suppress the angle random error caused by multipath and achieve predictive tracking of the target motion trajectory;

[0208] Step S7: When it is detected that the target has entered the critical landing phase, the multipath effect compensation mode is started. By building a real-time multipath propagation model, the phase and amplitude of the received signal are compensated to improve the tracking accuracy.

[0209] As a specific implementation method

[0210] The method proposed in the present invention for reducing the multipath effect of take-off and landing guidance radar based on adaptive off-axis tracking achieves effective suppression of multipath interference through the deep integration of hardware platform and intelligent algorithm.

[0211] Figure 2 This figure shows the geometric model of multipath effects for a takeoff and landing guidance radar. The radar altitude is hr, the target altitude is ht, and the horizontal distance is d. A direct wave reaches the radar directly from the target, while a reflected wave reaches the radar after reflecting off the ground. Using the mirror principle, ground reflections are treated as direct radiation from the mirrored target, simplifying multipath analysis.

[0212] The entire system utilizes a distributed processing architecture. The main controller uses an Intel Xeon E5-2680 v4 processor with a clock speed of 2.4 GHz and 64 GB of DDR4-2400 ECC memory. To support real-time inference of deep learning algorithms, the system is equipped with an NVIDIA Tesla V100 GPU, featuring 5120 CUDA cores and 16 GB of HBM2 memory. The signal processing unit utilizes a TiTMS320C6678 multi-core floating-point DSP with eight C66x cores running at 1.25 GHz, coupled with a Xilinx Kintex-7 XC7K325T FPGA for parallel processing.

[0213] The software system is built on a real-time Linux kernel, with preemption latency controlled within 50 microseconds. The entire software architecture consists of five layers: a hardware abstraction layer encapsulating various device interfaces, an operating system layer providing real-time scheduling, a middleware layer responsible for data management and communication, an application layer implementing core algorithms, and a user interface layer providing human-computer interaction. High-speed data transmission between modules is achieved via PCIe, Gigabit Ethernet, and CAN buses.

[0214] Implementation of multi-dimensional signal feature extraction technology

[0215] Traditional multipath detection methods mainly rely on signal amplitude changes, are easily affected by noise and have limited accuracy. The present invention constructs a complete multipath signal feature space through joint analysis of the time domain, frequency domain, spatial domain and polarization domain.

[0216] In the time domain, the system first samples the received direct signal and multipath signal at 80MHz with a quantization accuracy of 14 bits. The delay difference is accurately measured by calculating the cross-correlation function of the two signals. Specifically, let the direct signal be s1(t) and the multipath signal be s2(t). The cross-correlation function is defined as

[0217] R 12 (τ) = ∫s1(t)s2*(t-τ)dt,

[0218] Where τ is the time delay parameter and * represents the complex conjugate. By finding R 12 The peak position of (τ) determines the delay difference, and parabolic interpolation is performed around the peak to improve measurement accuracy. This method can improve the delay measurement accuracy from 8 nanosecond sampling interval accuracy to sub-nanosecond level.

[0219] In order to analyze the impact of multipath on pulse shape, the system uses Hilbert transform to extract the signal envelope. For the complex signal s(t), its analytical signal is s a (t) = s(t) + jH[s(t)], where H[s(t)] is the Hilbert transform of s(t). The signal envelope is defined as |sa (t)|. By comparing the envelope characteristics of the direct signal and the multipath signal, the pulse width change rate is calculated. The pulse width is defined as the time width corresponding to the envelope amplitude dropping to 50% of the peak value. The change rate calculation formula is (T multipath - T direct ) / T direct .

[0220] Time correlation analysis uses a sliding window technique, with a window length of 10 pulse repetition periods and a sliding step of 1 period. The normalized correlation coefficient is calculated as ρ = E[s1s2*] / √(E[|s1|²]E[|s2|²]), where E[] represents the mathematical expectation. When ρ < 0.7, the system determines that significant multipath is present.

[0221] Frequency domain analysis uses a 2048-point fast Fourier transform. To reduce spectral leakage, a Hamming window is applied to the signal before the transform, with the window function w(n) = 0.54 - 0.46cos(2πn / N). The frequency resolution reaches PRF / 2048, where PRF is the pulse repetition frequency. By analyzing the distribution characteristics of the power spectral density, parameters such as Doppler shift, spectral centroid, and spectral width are extracted. The Doppler shift fd = 2vr / λ reflects the radial velocity of the target, and the spectral centroid is λ. Characterizes the center of gravity of the spectrum. Multipath effects can cause spectrum broadening and center of gravity shift. These characteristics can serve as important basis for multipath identification.

[0222] Spatial processing uses an improved multiple signal classification algorithm to achieve high-precision arrival angle estimation. First, an 8×8 spatial covariance matrix R is constructed, where , X(t) is the received signal vector of 8 array elements, Conjugate transpose of . Perform eigenvalue decomposition on the covariance matrix , where Λ is the eigenvalue diagonal matrix and U is the eigenvector matrix. Assuming there are K signal sources, the first K largest eigenvalues ​​correspond to the signal subspace, and the rest correspond to the noise subspace En.

[0223] The core idea of ​​the MUSIC algorithm is to use the characteristics of the signal steering vector and the noise subspace being orthogonal. The steering vector is defined as , where d is the array element spacing, N is the number of array elements, and θ is the angle of arrival. The MUSIC spectrum function is By searching P MUSIC The peak value of (θ) can be used to estimate the signal arrival angle. The sharper the peak value, the higher the estimation accuracy.

[0224] To further improve the accuracy, the system uses the root MUSIC algorithm to solve the polynomial The angle of arrival is directly obtained by taking the root of the polynomial, avoiding the angle search process. The root of the polynomial gives the angle information in the form z = e^(j2πd sinθ / λ). Combined with parabolic interpolation technology, the angle estimation accuracy is ultimately improved to 0.01 degrees.

[0225] Polarization domain analysis is achieved by simultaneously measuring the horizontal H and vertical V polarization components. The polarization ratio is defined as ρ = EV / EH, where EV and EH are the vertically and horizontally polarized electric field intensities, respectively. The polarization ellipticity is calculated as ε = tan(χ) = Im(ρ) / Re(ρ), where χ is the ellipticity angle. Because ground reflection changes the polarization state of electromagnetic waves, the polarization characteristics of multipath signals differ significantly from those of direct signals, providing a new criterion for multipath identification.

[0226] Ultimately, the features extracted from the time, frequency, spatial, and polarization domains are combined into a 6-dimensional feature vector F = [Δt, ΔT / T, fd, θ, φ, ε]. To reduce computational complexity and remove redundant information, principal component analysis is used to reduce the dimensionality of the feature vector to 4 dimensions, retaining 95% of the variance. This reduced feature vector serves as input for subsequent machine learning algorithms.

[0227] Traditional radar systems use a passive response strategy based on deep learning-based multipath prediction, taking action only when multipath has already impacted tracking performance. This invention, by establishing a deep learning prediction model, can predict the changing trend of multipath effects 3-5 scanning cycles in advance, enabling proactive prevention.

[0228] The collection of training data is crucial to the success of the prediction model. The system establishes a long-term data collection mechanism, continuously acquiring data across different seasons, weather conditions, time periods, and target types. Ten samples are collected per second for 30 consecutive days, resulting in a large-scale dataset of approximately 26 million training samples. Input features include 11 dimensions: radar altitude hr, target altitude ht, slant range R, elevation angle θ, azimuth angle φ, signal strength S, phase difference Δφ, weather code W, ground reflection coefficient ρ, wind speed v, and relative humidity H. The output labels include three prediction targets: multipath intensity Mp, phase difference Δφmp, and time delay difference Δt.

[0229] Data preprocessing begins with outlier detection and cleaning, using the 3σ criterion and interquartile range method to remove data points with obvious errors. Then, data is normalized using the Z-score method: x' = (x - μ) / σ, where μ is the mean and σ is the standard deviation. To enhance the model's generalization, the system implements a data augmentation strategy: Gaussian white noise with a standard deviation of 5% is added to the original data, random jitter of ±0.05 seconds is applied in the time dimension, and new samples are generated by linear interpolation between adjacent samples. The dataset is divided into training, validation, and test sets in a ratio of 7:2:1.

[0230] The deep neural network adopts a three-layer fully connected architecture. The input layer contains 64 neurons, corresponding to the expanded feature vector. The first hidden layer has 128 neurons, the second hidden layer has 64 neurons, and the output layer has 3 neurons corresponding to the predicted target. The number of neurons in the network is determined by the empirical formula n = √(input nodes × output nodes) + α, where α∈[1,10] is a tuning constant. This is optimized within the range [64,128,256] using grid search.

[0231] Batch normalization and dropout layers are added after each hidden layer. Batch normalization accelerates training convergence by normalizing the mean and variance of each batch of input data. The calculation formula is y = γ(x-μ) / σ + β, where γ and β are learnable parameters. The dropout layer randomly sets the outputs of 30% of the neurons to zero to prevent overfitting. The activation function in the hidden layer uses the ReLU function f(x) = max(0, x), which has the advantages of simple calculation and fast convergence. The output layer uses the sigmoid function f(x) = 1 / (1+e^(-x)) to ensure that the output values ​​are in the range [0, 1].

[0232] The loss function is designed as a combination of mean squared error and L2 regularization: L = (1 / m)Σ(yi - ŷi)² + λΣwi², where m is the batch size, λ = 0.001 is the regularization coefficient, and wi is the network weight. The regularization term prevents overfitting caused by excessive weights. The optimizer uses the Adam algorithm, which combines the advantages of momentum and RMSprop, with parameters set to β1 = 0.9, β2 = 0.999, and ε = 1e-8. The learning rate uses an exponential decay strategy, starting at 0.001 and decaying by 5% every 100 epochs, according to the formula lr(t) = lr0 × 0.95^(t / 100).

[0233] During training, an early stopping mechanism is used to prevent overfitting. The system monitors the validation set loss and automatically stops training if the validation loss does not decrease for 20 consecutive epochs. Gradient clipping is also used to limit the gradient norm to less than 1.0 to prevent gradient explosion. The batch size is set to 32, and the maximum number of training epochs is 500.

[0234] To learn the temporal variations of multipath effects, the system designed a specialized LSTM network. LSTM effectively processes long sequences of data and addresses the vanishing gradient problem of traditional RNNs. The network input is a time series of length 10, with each time step containing a 64-dimensional feature vector. The LSTM layer contains 50 hidden units, sufficient to capture the temporal dependencies of multipath effects.

[0235] The internal structure of the LSTM unit contains three gating mechanisms: the forget gate determines what information to discard from the cell state, and the calculation formula is f t = σ(W f ·[h t -1, x t ] + b f ); the input gate decides what new information to store, i t = σ(W i ·[h t-1 , x t ] + b i ), candidate value C̃ t = tanh(WC·[h t-1 , x t ] + b C ); output gate controls output content, o t = σ(W o ·[h t-1 , x t ] + b o ). The cell state is updated to C t = f t * C t-1 + i t * C̃ t , the hidden state is h t = o t * tanh(C t ). Where σ is the Sigmoid function, W is the weight matrix, and b is the bias vector.

[0236] In order to improve the model's attention to key moments, an attention mechanism is integrated after the LSTM layer. The attention score is calculated as e t = tanh(W a ·h t + b a ), the attention weight is αt = exp(e t ) / Σexp(e j ), the context vector is c = Σα t ·h t This mechanism can automatically identify the most important time steps for the prediction results and improve the prediction accuracy.

[0237] The training parameters of the LSTM network include: batch size 32, dropout probability 0.2, gradient clipping threshold 1.0, and early stopping patience 20. The network uses the same Adam optimizer and learning rate strategy as the DNN.

[0238] The final prediction output is obtained by fusing the results of the deep neural network and the LSTM network. The fusion formula is Mp(t+k) = α·DNN_output + (1-α)·LSTM_output, where k = 3-5 is the prediction step size and α is the fusion weight. The optimal weight α = 0.6 was determined through 5-fold cross-validation. The fused prediction results are denormalized to restore them to the actual numerical range of the physical quantity and undergo a rationality check to ensure that the predicted values ​​are within the physical constraints.

[0239] Model performance is evaluated using multiple metrics: root mean square error (RMSE) = √[(1 / m)Σ(yi - ŷi)²] < 0.1, mean absolute error (MAE) = (1 / m)Σ|yi - ŷi| < 0.05, and coefficient of determination (R²) = 1 - SS_res / SS_tot > 0.9. The trained model can predict multipath changes over the next three to five scanning cycles with 95% confidence.

[0240] Intelligent off-axis tracking strategy

[0241] Traditional off-axis tracking methods use a fixed off-axis angle and are unable to adapt to dynamically changing multipath environments. This paper proposes an intelligent dynamic off-axis strategy that adaptively adjusts the off-axis angle based on real-time environmental conditions and target status, suppressing multipath effects while minimizing the impact on tracking accuracy.

[0242] First, a precise geometric model is established to describe the spatial relationship between the radar, target, and ground reflection. Let the radar altitude be hr, the target altitude be ht, and the horizontal distance between the target and the radar be d. The direct path length is R1 = √[d² + (ht-hr)²], and the reflected path length is R2 = √[d² + (ht+hr)²]. Using the mirror principle, the ground reflection is equivalent to a direct wave from a mirror target, with the mirror target position being (x, y, -ht). This approach transforms the complex reflection problem into a simple geometric problem.

[0243] The phase difference between the multipath signal and the direct signal is a key parameter for off-axis angle optimization. Based on Fresnel reflection theory, the phase difference is calculated as Δφ = (4π / λ)·hr·ht·sin(θ) / R, where θ is the radar elevation angle, λ is the radar operating wavelength, and R is the target range. Under the small-angle approximation, sin(θ) ≈ θ, so the phase difference is approximately proportional to the elevation angle.

[0244] The ground reflection coefficient is calculated according to the Fresnel formula, taking into account the complex dielectric constant of the ground material. For horizontally polarized waves, the reflection coefficient is ρ h = (cosθ i -√(ε r - sin²θ i )) / (cosθ i + √(ε r - sin²θ i )), where θ i is the angle of incidence, ε r is the complex relative dielectric constant of the ground. Different ground materials have different dielectric constants: concrete ε r = 6.0-j0.5, asphalt εr = 3.0-j0.2, grass εr = 2.5-j0.1, water surface ε r = 81.0-j0.1. The system selects the corresponding parameter value based on the actual ground conditions of the airport.

[0245] Determining the optimal off-axis angle requires finding a balance between multipath suppression and tracking performance loss. The objective function is designed as F(θ) = w1·Gm(θ) + w2·Gt(θ), where Gm(θ) is the multipath suppression gain, Gt(θ) is the tracking performance factor, and w1 and w2 are weight coefficients.

[0246] The multipath mitigation gain is defined as Gm(θ) = -20log|1 + ρe^(jΔφ(θ))|, which represents the multipath attenuation relative to on-axis tracking at an off-axis angle θ, expressed in dB. When the phase difference between the direct and multipath signals is an odd multiple of π, they destructively interfere, minimizing the impact of multipath. The tracking performance factor, defined as Gt(θ) = exp(-θ² / 2σ²), represents the tracking accuracy loss due to off-axis tracking. σ = 0.5° is an empirical parameter determined based on the 3dB beamwidth of the antenna pattern.

[0247] The selection of weight coefficients w1=0.7 and w2=0.3 is based on the optimization results of a large number of simulation experiments. A larger w1 weight reflects the importance of multipath suppression, while a proper w2 weight ensures that tracking accuracy is not excessively degraded.

[0248] The optimal off-axis angle is determined using the golden section method, a highly efficient single-variable optimization algorithm. The search interval is set to [0.2°, 1.8°]. The lower limit of 0.2° ensures a certain off-axis effect, and the upper limit of 1.8° is determined based on the antenna's 3dB beamwidth. Exceeding this range severely affects tracking accuracy.

[0249] The basic principle of the golden section method is to select trial points within the search interval according to the golden ratio φ = (1+√5) / 2 ≈ 1.618. Let the search interval be [a, b], and the two trial points be x1 = a + (1-1 / φ)(ba) and x2 = a + (1 / φ)(ba). The function f(x1) and f(x2) are compared, and the subinterval with the larger function value is retained for further search. The algorithm converges when the search interval width is less than 0.01° or the number of iterations exceeds 100. This method has the advantages of fast convergence and does not require derivative calculations, making it suitable for real-time applications.

[0250] Real-time angle control requires consideration of the physical constraints of the servo system. The system's maximum angular velocity is limited to 0.5° / s, based on the bandwidth characteristics of the antenna servo system. Angle updates are performed using a rate-limited algorithm: θ(t+1) = θ(t) +sign(Δθ)·min(|Δθ|, ωmax·Δt), where Δθ = θoptimal - θcurrent is the difference between the target and current angles, ωmax is the maximum angular velocity, and Δt is the sampling interval of 0.1 seconds.

[0251] To further smooth angle variations, the system uses a third-order Butterworth low-pass filter to filter the angle commands. The filter's transfer function is H(s) = ωc³ / (s³ + 2ωcs² + 2ωc²s + ωc³), where ωc = 2π × 0.1 is the cutoff frequency, corresponding to a cutoff frequency of 0.1 Hz. This cutoff frequency was selected based on target maneuver spectrum analysis; typical maneuvering frequencies for civil aircraft are less than 0.1 Hz.

[0252] The digital filter is implemented using a bilinear transformation: s = (2 / T)·(1-z^(-1)) / (1+z^(-1)), where T is the sampling period. The filter's differential equation is y(n) = Σbi·x(ni) - Σai·y(ni), where bi and ai are the filter coefficients. This design effectively suppresses high-frequency noise and prevents oscillation in the antenna system.

[0253] An adaptive parameter adjustment mechanism dynamically adjusts control parameters based on environmental changes and target motion. When a target maneuver is detected, the system increases its response speed to quickly track the target. During stable tracking, the system decreases its response speed to improve tracking smoothness. Maneuver detection is achieved by monitoring target acceleration, with acceleration exceeding 0.2 m / s² considered a maneuver.

[0254] Sudden environmental changes are detected by comparing the current multipath intensity with the historical mean. When |Mp(t) - μhistorical| > 3σhistorical, the system determines that a sudden environmental change has occurred and triggers a rapid recalculation of parameters. This recalculation must take less than 0.1 seconds to ensure the system can respond promptly to environmental changes.

[0255] False target identification and verification

[0256] Multipath not only affects the tracking accuracy of real targets but can also create false targets, disrupting radar operation. Traditional methods primarily rely on signal amplitude to identify false targets, which can easily lead to misjudgments. This paper proposes a multi-dimensional joint verification method that accurately identifies false targets through a comprehensive analysis of signal coherence, trajectory consistency, and RCS characteristics.

[0257] Signal coherence detection is based on the correlation characteristics of the direct signal and multipath signals. The coherence time is calculated by calculating the width of the cross-correlation function between the two signals and is defined as the time span when the amplitude of the correlation function drops to 1 / e of its peak value. The coherence time is inversely proportional to the signal bandwidth: Tc ≈ 1 / B, where B is the effective bandwidth of the signal. The coherence time of a real target is typically long and stable, while the coherence time of a multipath false target can be significantly shortened due to the complexity of the propagation path.

[0258] The coherence bandwidth is obtained by estimating the signal's power spectral density using the Welch method. The specific steps are: divide the signal into segments, each with 1024 sampling points and a 50% overlap; apply a Hanning window to each segment and perform a FFT transform; and calculate the average power spectrum of each segment to estimate the power spectral density. The coherence bandwidth is defined as the frequency width at which the power spectral density amplitude drops to 50% of its peak value. Multipath effects can broaden the power spectrum and reduce the coherence bandwidth.

[0259] The formula for calculating the coherence coefficient is ρc = max|R12(τ)| / √[R11(0)R22(0)], where R12(τ) is the cross-correlation function of the two signals, and R11(0) and R22(0) are the autocorrelation values ​​of the two signals at zero time delay. The coherence coefficient reflects the degree of similarity between the two signals and ranges from [0 to 1]. Through statistical analysis of a large amount of measured data, the judgment threshold is determined to be 0.7. When the coherence coefficient falls below this threshold, the system determines it as a false target.

[0260] Trajectory consistency verification uses Kalman filtering technology to establish a target motion model. The state vector is defined as X = [x, vx, y, vy]T, which contains the position and velocity of the target in the Cartesian coordinate system. The state transition model uses the uniform linear motion assumption, and the state transition matrix is:

[0261] F = [[1, Δt, 0, 0], [0, 1, 0, 0], [0, 0, 1, Δt], [0, 0, 0, 1]]

[0262] Where Δt = 0.1s is the sampling interval.

[0263] The process noise covariance matrix Q is designed using the Singer maneuver model to reflect the uncertainty of target motion. The matrix elements are: Q11 = Q33 = qΔt 4 / 4, Q12 = Q21 = Q34 = Q43 = qΔt³ / 2, Q22 = Q44 = qΔt², and the other elements are 0. q is the maneuver intensity parameter, which is set to 0.1m / s² for civil airliners, corresponding to the minor maneuvers during normal flight.

[0264] The observation model converts the Cartesian coordinates of the target into the polar coordinates of the radar. The observation vector Z = [r, θ]T, where r is the distance and θ is the angle. The observation equation is: r = √(x² + y²) θ = arctan(y / x)

[0265] The observation noise covariance matrix R = diag[σr², σθ²], where σr is the standard deviation of the distance measurement noise and σθ is the standard deviation of the angle measurement noise, which is determined by the radar system accuracy.

[0266] The prediction step of the Kalman filter is: x̂(k|k-1) = Fx̂(k-1|k-1) P(k|k-1) = FP(k-1|k-1)FT + Q

[0267] The update procedure is: ν(k) = z(k) - h[x̂(k|k-1)] S(k) = H(k)P(k|k-1)HT(k) + RK(k) = P(k|k-1)HT(k)S-1(k) x̂(k|k) = x̂(k|k-1) + K(k)ν(k) P(k|k) = [I - K(k)H(k)]P(k|k-1)

[0268] Where ν(k) is the innovation vector, S(k) is the innovation covariance, K(k) is the Kalman gain, and H(k) is the Jacobian matrix of the observation matrix.

[0269] Innovation verification is performed using standardized innovation νs = S-1 / 2ν. Ideally, standardized innovation follows a standard normal distribution. Using the 3σ criterion, a trajectory anomaly is determined when |νs| > 3. To improve verification robustness, the system maintains a 5-frame historical data window and verifies the authenticity of the target through correlation analysis of multiple frames.

[0270] The multi-frame correlation formula is A = Σwi·ai, where wi = exp(-i / τ) is the temporal weighting factor, τ = 2 is the time constant, and ai is the correlation index for the i-th frame. True targets exhibit good correlation across multiple frames, with correlation typically exceeding 0.6; false targets, on the other hand, often appear intermittently and have a lower correlation.

[0271] Radar cross-section (RCS) characteristic analysis is a key tool for false target identification. The system has established an RCS database for 20 typical civil airliners, including major models such as the A320, B737, C919, and A380. RCS data for each aircraft model covers 360° in azimuth and an elevation range of -10° to +30°, with an angular resolution of 1°. RCS modeling uses the empirical formula σ(θ,φ) =σ0·P(θ,φ), where σ0 is the average RCS value and P(θ,φ) is the normalized pattern function. This pattern function is based on the aircraft's geometry and primary scattering sources, taking into account the contributions of components such as the fuselage, wings, and tail.

[0272] Real-time RCS measurement is calculated using the radar equation: σ = (Pr·R 4 ·(4π)³) / (Pt·Gt·Gr·λ²), where Pr is the received power, Pt is the transmitted power, Gt and Gr are the transmitting and receiving antenna gains, respectively, R is the target distance, and λ is the operating wavelength. To improve measurement accuracy, the system accumulates and averages multiple pulses, while also correcting for factors such as atmospheric attenuation and precipitation attenuation. RCS measurement accuracy is required to reach ±1dB.

[0273] Anomaly detection is achieved by comparing the measured RCS with the theoretical value in the database. The anomaly index (AI) is defined as |σmeasured - σexpected| / σexpected, where σexpected is obtained from a database lookup based on the target recognition result and the current attitude angle. A two-level threshold is used: AI > 0.4 marks the target as suspicious and requires further verification; AI > 0.7 is directly classified as an anomaly. Multipath effects often cause abnormal increases or decreases in RCS measurements. RCS anomaly detection can effectively identify false multipath targets.

[0274] Polarimetric analysis is achieved by simultaneously measuring the horizontally and vertically polarized scattering characteristics of a target. The polarization ratio (PR) is calculated as σVV / σHH, where σVV and σHH represent the vertically and horizontally polarized RCS, respectively. For metallic targets such as aircraft, the polarization ratio typically ranges from 0.1 to 3.5. A polarization ratio outside this range may indicate multipath effects or target anomalies.

[0275] Angular scintillation detection is achieved by analyzing the temporal variation of RCS. The angular scintillation index (AS) is defined as σRCS / μRCS, where σRCS is the standard deviation of the RCS measurements and μRCS is the mean. The angular scintillation index of a normal target is typically less than 0.3, while the AS value of a target affected by multipath may exceed 0.6.

[0276] Comprehensive judgment utilizes a multi-dimensional feature fusion approach. The coherence detection result Cc, the trajectory consistency verification result Ct, and the RCS characteristic analysis result Cs are weighted and fused: C = w1·Cc + w2·Ct + w3·Cs, where the weight coefficients w1=0.4, w2=0.3, and w3=0.3. This weight distribution is determined based on the reliability and complementarity of the various methods. The final confidence level C ranges from [0 to 1], and the judgment threshold is set at 0.75. When C < 0.75, the system determines it as a false target.

[0277] The adaptive threshold adjustment mechanism dynamically adjusts the decision threshold based on environmental conditions. In environments with strong multipath effects, the system appropriately lowers the threshold to improve false target detection sensitivity; in relatively clean environments, the threshold is raised to reduce false positives. Threshold adjustment is based on a sliding window with a window length of 100 scan cycles. The mean μ and standard deviation σ of the environmental multipath intensity are calculated. The adjusted threshold is Th_adjusted = Th_default - k (μ - μnominal) / σnominal, where k = 0.1 is the adjustment factor.

[0278] Real-time multipath compensation technology

[0279] In addition to avoiding multipath effects through off-axis tracking, the system further suppresses multipath effects through active compensation technology, which includes three-dimensional environment modeling, ray tracing calculations, adaptive beamforming, and time-domain equalization.

[0280] Three-dimensional environmental modeling is the foundation of multipath compensation. The system draws on multiple data sources to create a high-precision three-dimensional environmental model of the airport's perimeter. Terrain data is obtained through lidar measurements, with a horizontal resolution of 5m x 5m and an elevation accuracy of ±0.5m. Building data is obtained through a combination of aerial photography and on-site mapping, with a three-dimensional geometric accuracy of ±1m. Ground material distribution is determined through high-resolution remote sensing imagery interpretation and on-site surveys. A database of 15 typical materials, including concrete, asphalt, grass, gravel, metal, and water, is established, each corresponding to a different complex dielectric constant.

[0281] The environmental database utilizes a hierarchical dynamic update strategy. Static data, such as topography and major buildings, is updated annually; semi-static data, such as seasonal vegetation changes, is updated quarterly; and dynamic data, such as meteorological parameters, is updated in real time. Update triggers include the arrival of scheduled events, environmental change detection, and performance deviation exceeding limits. Data updates are incremental, modifying only the changed parts to improve update efficiency.

[0282] The ray tracing algorithm calculates the propagation path of electromagnetic waves based on geometric optics approximation. In the millimeter wave band, where wavelengths are much smaller than the size of objects in the environment, the geometric optics approximation offers excellent accuracy. The algorithm considers reflection, refraction, and scattering of electromagnetic waves at interfaces such as the ground and buildings, setting the maximum number of reflections to three to balance computational accuracy and complexity.

[0283] Reflection path search is implemented using the mirror method. For planar reflective interfaces, the reflection path is determined by constructing a mirror image of the emission point about the reflective surface. For multiple reflections, the mirror method is recursively applied to calculate the positions of each mirror. The reflection coefficient is calculated based on the Fresnel formula, taking into account the angle of incidence, polarization, and interface material properties. For ideal conductors, the reflection coefficient is close to -1; for lossy media, the reflection coefficient has a magnitude less than 1 and exhibits a phase delay.

[0284] The losses in each propagation path include free-space propagation loss, interface reflection loss, and atmospheric absorption loss. Free-space propagation loss, Lfs, = 20log(4πR / λ), where R is the propagation distance. Reflection loss, Lr, = -20log|ρ|, where ρ is the reflection coefficient. Atmospheric absorption loss, La, = α·R, where α is the absorption coefficient, is approximately 0.02 dB / km at 77 GHz.

[0285] The atmospheric refraction effect is taken into account by using a modified refractive index model. The atmospheric refractive index varies with altitude as n(h) = 1+ 77.6×10⁻6 (P / T + 4810e / T²), where P is atmospheric pressure, T is absolute temperature, e is water vapor pressure, and h is altitude. Under standard atmospheric conditions, the refractive index gradient is approximately -40×10⁻ 6 / m. The ray path is determined by solving the ray equation, taking into account the path bending caused by refraction.

[0286] Adaptive beamforming technology adjusts the amplitude and phase weights of each element in the antenna array to form a main lobe in the direction of the desired signal and a null in the direction of the interfering signal. The weight vector is calculated using the minimum mean square error criterion, with the objective function min E[|d(n) - wᴴx(n)|²], where d(n) is the desired signal, x(n) is the received signal vector, and w is the weight vector.

[0287] In practical implementation, a linearly constrained minimum variance algorithm is used. Constraints include maintaining unity gain in the mainlobe direction: wᴴa(θ0) = 1, where a(θ0) is the steering vector in the desired direction; and a nulling depth constraint: |wᴴa(θᵢ)| ≤ ε, where θᵢ is the interference direction and ε is the nulling depth threshold. The optimization problem is formulated as: min wᴴRw subject to Cᴴw = f, where R is the received signal covariance matrix, C is the constraint matrix, and f is the constraint vector.

[0288] The Lagrange multiplier method solves the optimal weight vector: w = R⁻¹C(CᴴR⁻¹C)⁻¹f. To avoid the large amount of matrix inversion calculations, the system uses a recursive least squares algorithm to achieve real-time weight updates. The recursive formula of the RLS algorithm is:

[0289] K(n) = P(n-1)x(n) / (λ + xᴴ(n)P(n-1)x(n)) P(n) = (1 / λ)[P(n-1) - K(n)xᴴ(n)P(n-1)] w(n) = w(n-1) + K(n)[d*(n) - xᴴ(n)w(n-1)]

[0290] Where λ is the forgetting factor, which takes a value of 0.99 and balances the convergence speed and steady-state performance of the algorithm.

[0291] To prevent system instability caused by excessively large weight vectors, a diagonal loading is added: R → R + δI, where δ is the loading coefficient and I is the identity matrix. The loading coefficient is set to 10% of the received noise power.

[0292] Time-domain equalization is used to compensate for intersymbol interference caused by multipath. The system uses a 32nd-order finite impulse response adaptive equalizer. The equalizer output is y(n) = Σ(i=0 to N-1) wᵢx(ni), where wᵢ is the weight coefficient of the i-th tap and N=32 is the number of taps.

[0293] The equalizer weights are adaptively updated using the least mean square algorithm: w(n+1) = w(n) + μe*(n)x(n), where μ is the step size parameter, e(n) = d(n) - y(n) is the error signal, and d(n) is the desired signal. The step size parameter is chosen to balance convergence speed and steady-state error, and is set to μ = 0.01.

[0294] To further improve equalization performance, the system employs a decision-feedback equalizer architecture consisting of a feedforward filter and a feedback filter. The feedforward filter processes current and future input signals and has 16 taps. The feedback filter uses already-decided symbols to eliminate interference with subsequent symbols and has 16 taps. This decision-feedback architecture effectively handles post-multipath and improves equalization.

[0295] The equalizer's convergence performance is evaluated by monitoring the mean square error (MSE(n)) = E[|e(n)|²]. When the MSE remains below -30 dB, the equalizer is considered to have converged to a steady state. To accelerate convergence, the system uses a larger step size of 0.05 in the initial stage, which is then reduced to 0.01 after convergence to maintain steady-state performance.

[0296] The real-time evaluation of the compensation effect is achieved through multiple performance indicators. The signal-to-interference-and-noise ratio improvement is defined as SINR_gain = 10log 10 [(S / I+N)after / (S / I+N)before], where S is the signal power, I is the interference power, and N is the noise power. Tracking error reduction rate (ER) = (σbefore - σafter) / σbefore, where σ is the standard deviation of the tracking error. False alarm rate reduction (VR) = (FAbefore - FAafter) / FAbefore, where FA is the false alarm rate.

[0297] The target performance indicators are set as follows: SINR improvement ≥ 6dB, error reduction rate ≥ 40%, and false alarm rate reduction ≥ 60%. If any indicator falls below the target value, the system automatically adjusts the compensation parameters or switches the compensation strategy.

[0298] Environmental Adaptive Learning and Optimization

[0299] To adapt to changing environmental conditions, the system has established an environmental adaptive learning mechanism that continuously optimizes model parameters based on long-term observation data, improving the accuracy of prediction and compensation.

[0300] The system has a library of typical scenarios tailored to different seasons and weather conditions. These include mild spring weather (10-20°C, 60-80% humidity), hot summer weather (25-35°C, 40-60% humidity), dry autumn weather (5-15°C, 30-50% humidity), cold winter weather (-5 to 5°C, 50-70% humidity), rainy and humid weather (precipitation >5 mm / h, humidity >85%), foggy and hazy weather (visibility <1 km), and strong winds (wind speed >10 m / s). Each scenario corresponds to specific multipath distribution characteristics and propagation parameters.

[0301] Scene recognition is automatically determined based on real-time meteorological data. Meteorological parameters include temperature, humidity, air pressure, wind speed, wind direction, precipitation, and visibility. Scene recognition uses a fuzzy clustering algorithm to match the current meteorological parameter vector with the characteristic vectors of typical scenes and select the scene with the highest similarity. This similarity is calculated using the Euclidean distance: d = √[Σ(xi -yi)²], where xi represents the current parameter and yi represents the scene characteristic parameter.

[0302] The online learning algorithm uses gradient descent to optimize model parameters. The parameter update formula is θ(t+1) = θ(t) - η(t)∇J(θ(t)), where η(t) is the learning rate and J is the loss function. The learning rate is adaptively adjusted: η(t) = η0 / (1 + αt + β|∇J|), where η0 = 0.01 is the initial learning rate, and α = 0.001 and β = 0.1 are adjustment parameters. Increasing the learning rate accelerates convergence when the prediction error decreases, while decreasing it improves stability when the error increases.

[0303] The model was validated using a sliding window cross-validation method. The most recent 1000 samples were divided into a training set and a validation set. The training set was used for parameter updates, and the validation set was used for performance evaluation. The window was slid by 100 samples at a time to maintain data freshness. Model performance was evaluated using the root mean square error (RMSE) and mean absolute percentage error (MAPE).

[0304] The system maintains multiple candidate models, including linear regression, polynomial regression, neural networks, and other models of varying complexity. It automatically selects the most appropriate model based on current environmental conditions and data characteristics. Model selection is based on information criteria, such as the Akaike Information Criterion (AIC) = 2k - 2ln(L), where k is the number of parameters and L is the likelihood function value. A smaller AIC value indicates a better model.

[0305] Anomaly detection uses statistical process control methods. A control chart for multipath intensity is created, with an upper control limit (UCL) = μ + 3σ and a lower control limit (LCL) = μ - 3σ, where μ and σ are calculated based on historical data. Anomaly criteria include: a single point outside the control limit, seven consecutive points on the same side of the centerline, and six consecutive points showing an upward or downward trend.

[0306] When an anomaly is detected, the system initiates a root cause analysis process. Possible sources of the anomaly include new buildings, ground construction, equipment failure, and sudden weather changes. The analysis method, based on a decision tree and expert system, combines the anomaly's temporal characteristics, spatial distribution, and intensity to determine the most likely cause.

[0307] Abnormal response mechanisms include rapid parameter calibration, model retraining, and activation of backup strategies. Response time requirements: abnormality detection < 5 seconds, cause analysis < 30 seconds, and parameter adjustment < 60 seconds. For abnormalities that cannot be quickly recovered, the system automatically switches to safe mode and adopts a conservative tracking strategy to ensure basic functionality.

[0308] Multi-radar collaboration and system integration

[0309] To further improve the reliability and performance of the system, the present invention supports multi-radar collaborative operation. The multi-radar system adopts a distributed deployment, with the main radar located on the extended runway centerline and 2-3 auxiliary radars distributed on both sides of the runway, with a radar spacing of 200-500 meters.

[0310] The optimization of multi-radar geometric layout is based on the principle of spatial diversity. When radars at different locations observe the same target, the impact of multipath varies. Information fusion can achieve better performance than a single radar. The baseline length, B, must satisfy the constraint of B > λR / (2ρh), where ρ is the required resolution and h is the target height.

[0311] Inter-radar interference coordination utilizes a strategy that combines time-division multiplexing (TDM) and frequency-division multiplexing (FDM). In TDM, each radar's transmission slots are staggered, with a slot interval of Δt = 2Rmax / c + τ, where Rmax is the maximum detection range, c is the speed of light, and τ = 10μs is the guard time. In FDM, the operating frequency spacing between adjacent radars is no less than twice the signal bandwidth, and frequency hopping is employed to further minimize interference.

[0312] Data association is a key technology for multi-radar collaboration. The system uses a probabilistic data association algorithm that takes into account target motion, observation error, and false alarm probability. The association gate is set based on the Mahalanobis distance: γ = (z - ẑ)ᵀS⁻¹(z - ẑ)<γth, where z is the observation vector, ẑ is the predicted observation, S is the innovation covariance matrix, and γth is the threshold value. The threshold value is determined by balancing the detection probability with the false alarm probability.

[0313] Multi-radar data fusion utilizes a combined centralized and distributed architecture. Each radar first performs local processing to extract target parameters and confidence information; the results are then sent to the fusion center for global optimization. The fusion algorithm uses a weighted least squares approach: x̂ = (Σ Wi)⁻¹(Σ Wi xi), where Wi = Pi⁻¹ is the weight matrix and Pi is the error covariance matrix of the i-th radar.

[0314] Weight allocation takes into account the radar's measurement accuracy, reliability, and multipath impact. Radars with high accuracy and low multipath impact receive greater weights. The dynamic weight adjustment formula is wi = (1 / σi²)·(1-Mpi)·Ri, where σi is the measurement error, Mpi is the multipath intensity, and Ri is the reliability factor.

[0315] The master handover mechanism dynamically selects the dominant radar based on the comprehensive performance of each radar. Performance evaluation metrics include signal-to-noise ratio, angular accuracy, multipath mitigation, and device health. A soft handover strategy is used to avoid sudden hard handovers that could cause tracking discontinuities.

[0316] The system integration adopts a modular design for easy expansion and maintenance. Key modules include signal processing, data processing, decision control, communications, and human-machine interface modules. Modules are connected via standardized interfaces, supporting hot swapping and online upgrades.

[0317] Real-time performance is a key requirement for system integration. Signal processing latency is <20ms, data fusion latency is <10ms, control instruction execution latency is <5ms, and total system latency is <50ms. Real-time performance is ensured through dedicated hardware acceleration, priority scheduling, and interrupt response optimization.

[0318] The fault-tolerant design utilizes a multi-layered redundancy strategy. Key hardware components utilize hot backup, while software utilizes exception handling and checkpoint recovery mechanisms. When a fault is detected, the system first attempts software recovery, then switches to backup hardware if this fails. In the worst-case scenario, it enters safe mode to maintain basic functionality.

[0319] System performance verification is conducted through a combination of simulation testing and actual flight tests. Simulation testing establishes a high-fidelity RF environment simulator capable of generating a variety of complex multipath scenarios and target motion trajectories. The simulator includes a signal generator, fading channel simulator, noise source, target motion simulator, and other equipment.

[0320] Typical scenarios covered by the simulation tests include: different weather conditions (sunny, rainy, foggy, snowy), different time periods (daytime, nighttime, dusk), different target types (large passenger aircraft, medium-sized passenger aircraft, small aircraft), different approach trajectories (straight-in approach, curved approach, missed approach), and different multipath intensities (mild, moderate, severe). For each scenario, 1,000 Monte Carlo simulations were performed, and performance indicators were statistically analyzed.

[0321] Actual flight tests were conducted at multiple airports, including large hubs, medium-sized airports, and high-altitude airports, encompassing diverse geographical environments and climatic conditions. Test aircraft included major models such as the A320, B737, and C919, ensuring the universal applicability of the verification results. During the tests, radar observation data, GPS ground truth data, and meteorological data were recorded for offline analysis and online performance evaluation.

[0322] Long-term operational validation is conducted in a real airport environment, with cumulative operation time exceeding one year and handling over 100,000 flights. During operation, system performance is continuously monitored, fault data and maintenance records are collected, and the system's reliability and maintainability are evaluated.

[0323] Test results show that compared with traditional methods, the proposed method significantly improves multipath suppression, tracking accuracy, and false target reduction. Multipath suppression is greater than 15dB, tracking accuracy is improved by more than 40%, false targets are reduced by more than 60%, and system availability exceeds 99.9%.

[0324] The present invention achieves comprehensive suppression of multipath effects through the organic integration of technologies such as multi-dimensional signal feature extraction, deep learning prediction, intelligent off-axis tracking, false target identification, and real-time multipath compensation, significantly improving the performance of take-off and landing guidance radar in complex environments and providing important guarantees for civil aviation flight safety.

[0325] Example 1: Multipath Suppression System Based on X-Band Takeoff and Landing Guidance Radar

[0326] This example uses the ILS precision approach radar system for Runway 36R at Beijing Capital International Airport as an example to illustrate the specific implementation of the present invention. The system operates at a 9.1 GHz frequency, uses an 8-element uniform linear array antenna with 1.67 cm element spacing, and is installed at a height of 12 meters. It is primarily used to guide the precision approach of typical passenger aircraft, such as the Boeing 737 and Airbus A320.

[0327] The system hardware configuration includes a dual-channel digital receiver (100MHz sampling rate), an FPGA+DSP signal processing platform (1.2GHz), and an industrial computer equipped with a GPU accelerator card (32GB of memory). The software adopts a modular architecture and includes core modules such as signal processing, feature extraction, machine learning prediction, off-axis control, false target recognition, and multipath compensation.

[0328] During the multidimensional signal feature extraction process, the system first performs high-speed sampling and digital down-conversion on the received radar signal. For time-domain feature extraction, a cross-correlation function with a sliding window length of 1024 sampling points is used to calculate the multipath delay difference. The direct signal is used as a reference template and a normalized cross-correlation operation is performed with the received signal. A valid multipath signal is identified when the correlation peak exceeds 0.3 and the delay is greater than 0. A Hilbert transform is also used to extract the signal envelope. The pulse width is determined at the 50% amplitude point, and the pulse width change rate is calculated as the standard deviation of 10 consecutive pulses.

[0329] Frequency domain feature extraction uses a 1024-point FFT transform with a frequency resolution of approximately 9.77 kHz. Doppler shift is determined by finding the frequency point with the maximum power spectrum, and the spectral centroid is calculated using a power-weighted average method. The power spectral density is normalized to the sampling frequency and the number of FFT points. Spectral broadening features are determined by calculating the power-weighted variance of each frequency point relative to the centroid frequency.

[0330] Spatial feature extraction constructs an 8×8 covariance matrix based on an 8-element uniform linear array. Eigenvalue decomposition is used to split the feature space into a signal subspace and a noise subspace. The MUSIC algorithm searches within the range of -90° to 90° with a step size of 0.1°, calculating the pseudospectral value at each angle. To improve accuracy, the root MUSIC algorithm is further employed. This algorithm constructs a Toeplitz matrix polynomial for the noise subspace, solves its roots, and selects roots within the unit circle to calculate the precise angle. Parabolic interpolation is performed at three points near the peak, improving angle accuracy to 0.01°.

[0331] Polarization feature extraction simultaneously receives two polarization components: horizontal (H) and vertical (V). The complex polarization ratio is defined as the complex ratio of the V component to the H component. Polarization ellipticity is calculated using the amplitude and phase difference between the two polarization components using the formula: ellipticity = arctan(2E_hE_v*sin(phase difference) / (E_h²-E_v²)) / 2, where E_h and E_v are the horizontal and vertical polarization electric field amplitudes, respectively. The polarization angle is calculated using a similar formula but using the cosine function.

[0332] After constructing the 6-dimensional feature vector, principal component analysis (PCA) was used for dimensionality reduction. The PCA model was pre-trained on a large amount of historical data, retaining principal components that contribute 95% of the cumulative variance. In practice, the variance contributions of the first four principal components were 35%, 28%, 18%, and 14%, respectively, effectively preserving the key information of the original features. The reduced 4-dimensional feature vector served as input for subsequent machine learning algorithms.

[0333] The machine learning prediction module first performs data preprocessing. Multipath data from various weather conditions, time periods, and aircraft models are collected to establish a training database containing 100,000 samples. During the data cleaning phase, invalid samples with signal-to-noise ratios below 10dB and abnormal multipath strength (exceeding three standard deviations from the historical mean) are removed. Data normalization uses Z-score standardization to scale each dimension to a distribution with a mean of 0 and a standard deviation of 1. The training, validation, and test sets are randomly split in a 7:2:1 ratio.

[0334] Data augmentation was achieved through three methods: (1) adding Gaussian white noise with a signal-to-noise ratio of 20dB; (2) multiplying the original data by a random factor of 0.8-1.2 to simulate time jitter; and (3) performing linear interpolation with a coefficient of 0.3-0.7 between adjacent samples to generate new samples. After augmentation, the amount of training data increased by four times.

[0335] The deep neural network uses a three-layer fully connected architecture: the input layer has 64 nodes corresponding to the reduced feature vectors, the first hidden layer has 128 nodes, the second hidden layer has 64 nodes, and the output layer has three nodes that predict the multipath strength Mp, phase difference Δφ, and delay difference Δt, respectively. Batch normalization layers are added between each layer to accelerate convergence, and dropout layers are used to prevent overfitting, with a dropout probability set to 0.3. Reinforced Luminance (ReLU) activation function is used, and linear activation is used in the output layer.

[0336] The loss function was designed as L = MSE + 0.001×Σwi², where MSE is the mean squared error and the second term is L2 regularization to prevent overfitting. Adam was used as the optimizer, with an initial learning rate of 0.001, β1=0.9, and β2=0.999. An early stopping mechanism was implemented during training; if the validation loss did not decrease for 10 consecutive epochs, training was terminated and the optimal weights were restored.

[0337] The LSTM time series network processes time series with a length of 10, an input feature dimension of 64, and 50 LSTM units in the hidden layer. The network structure consists of two LSTM layers, with the first layer returning the complete sequence and the second layer returning only the final output. To improve the ability to identify key moments, an attention mechanism is added after the LSTM output. A fully connected layer and a softmax function are used to calculate the weight of each moment and perform a weighted summation of the LSTM outputs.

[0338] In multi-model fusion prediction, the DNN network weight α1 = 0.6, and the LSTM network weight α2 = 0.4. The fusion prediction formula is Mp_pred(t+k) = 0.6 × DNN_out + 0.4 × LSTM_out, where k is the prediction step size, which is 3-5 radar scan cycles (4 seconds per cycle). When the DNN and LSTM prediction results differ significantly, the weights are dynamically adjusted based on the respective prediction confidence levels.

[0339] Dynamic threshold calculation maintains a sliding window of historical multipath intensity with a length of 100. The real-time threshold Th(t) = M_mean + 2.5 × M_std + 0.15 × |dM / dt|, where M_mean and M_std are the mean and standard deviation within the window, and dM / dt is the rate of change of multipath intensity. When the predicted multipath intensity exceeds the dynamic threshold, off-axis tracking mode is initiated 3-5 scan cycles in advance.

[0340] Intelligent elevation lock-on begins by establishing a three-dimensional geometric model of the radar, target, and ground. A coordinate system is established with the radar as the origin, with the target position (x, y, h), where x is the horizontal distance, y is the lateral distance, and h is the target height. The direct path length is R_direct = √(x²+y²+(h-h_r)²), and the reflected path length is R_reflect = √(x²+y²+(h+h_r)²), where h_r is the radar height of 12 meters. The mirrored target position is (x, y, -h), facilitating subsequent geometric calculations.

[0341] The ground reflection coefficient is calculated using the Fresnel formula, taking into account the complex dielectric constants of different materials. The relative dielectric constant of a concrete runway is εr = 6.0, and the electrical conductivity is σ = 0.01 S / m. The reflection coefficient Γ = (cosθi - √(εr-sin²θi)) / (cosθi + √(εr-sin²θi)), where θi is the angle of incidence. Actual calculations also need to account for environmental factors such as ground roughness and humidity, adjusting for these factors using correction factors.

[0342] The optimal off-axis angle is obtained by the objective function F opt (θx) = 0.7×G mp (θx) + 0.3×G track (θx) is solved, where G mp is the multipath suppression gain, G track is the tracking performance function. The multipath mitigation gain is determined by calculating the improvement in signal-to-interference ratio after off-axis deviation. The tracking performance function considers the impact of angular deviation on angle measurement accuracy. The golden section method is used to search for the optimal solution in the interval [0°, 2°], with a convergence accuracy of 0.01° and a maximum of 100 iterations to ensure real-time performance.

[0343] The off-axis angle dynamic constraints include the angular velocity limit |dθ / dt|≤0.7° / s and the angle range θ∈[0.2°,1.8°]. The angle command is smoothed by a 3rd-order Butterworth low-pass filter with a cutoff frequency of 0.1Hz to prevent the antenna system from oscillating. When the environmental change index ECI = |Mp cur -Mp pred | / σ predWhen >2.5, the trigger parameters are quickly recalculated and the update time does not exceed 2 seconds.

[0344] Multipath false target identification establishes a four-dimensional discrimination model. Coherence detection calculates the signal's coherence time and coherence bandwidth. Targets with a coherence coefficient below 0.6 are flagged as suspicious. Trajectory consistency is verified using a Kalman filter's innovation check. The state vector contains position and velocity information. Trajectory anomalies are identified when the innovation covariance exceeds a statistical threshold of 3σ. RCS characteristic analysis compares measured values ​​with theoretical models. Anomalies are identified when the anomaly index AI = |σm-σe| / σe>0.4. Multi-frame correlation analyzes target presence probability within a 10-second window, classifying intermittent targets as false.

[0345] The comprehensive confidence fusion formula is C total = 0.3×C coh + 0.3×C traj + 0.2×C rcs + 0.2×C prob , each confidence value is [0,1]. Adaptive decision threshold Th adapt = 0.75 - 0.1×Mp level + 0.05 × SNR factor , where Mp level is the current multipath strength level, SNR factor is the signal-to-noise ratio factor. When the comprehensive confidence is lower than the adaptive threshold, the target is marked as a false target and removed from the tracking list.

[0346] Adaptive Kalman filtering introduces multipath error compensation terms based on the traditional state equation. The state equation is X(k+1) = [I + 0.1×A + Δm comp (k)]X(k) + ΓU(k) + W(k), where Δm comp (k) Real-time estimation via neural network. The process noise and observation noise covariance matrices are estimated via two independent three-layer neural networks, with inputs including multipath strength, signal-to-noise ratio, target velocity, and other parameters.

[0347] Multi-model filtering establishes three motion models: uniform velocity (CV), uniform acceleration (CA), and uniform cornering (CT). Model probabilities are updated using the likelihood function: μi(k) = Li(k)μi(k-1) / Σj[Lj(k)μj(k-1)]. The likelihood function Li(k) is calculated based on the prediction residuals of each model. The final state estimate is a probability-weighted average of the outputs of the three models, effectively accounting for changes in motion patterns during target maneuvers.

[0348] Reinforcement learning uses Q-learning to optimize the Kalman gain. The state space includes 27 states, including multipath strength level (low / medium / high), signal-to-noise ratio level (low / medium / high), and prediction error level (small / medium / large). The action space is the gain adjustment, including increase, decrease, and hold. The reward function is defined based on the tracking error, with positive rewards for decreasing error and negative rewards for increasing error. A decreasing learning rate strategy, αlr(k) = 0.01 / (1+0.001×k), is used to ensure convergence.

[0349] Multipath compensation was used to create a 3D airport environmental model with a 5m x 5m grid resolution and a 2m height resolution. Topographic data was derived from airport construction drawings and laser scanning surveys. The building model includes precise geometric information for major structures such as the terminal, hangar, and control tower. The material property database contains electromagnetic parameters for 15 materials, including concrete, metal, and glass.

[0350] Ray tracing uses a geometric optics approximation to trace the propagation path of electromagnetic waves from transmitter to receiver. Up to three reflections are considered, and the reflection coefficient for each reflection is calculated based on material properties and the angle of incidence. Atmospheric refraction is calculated using a standard atmospheric model to calculate the vertical profile of the refractive index, and absorption attenuation takes into account the frequency-dependent properties of oxygen and water vapor. Ray tracing results include the time delay, amplitude, and phase information for each path.

[0351] Adaptive beamforming calculates the optimal weight vector w_ by the minimum variance distortionless response (MVDR) criterion beam =R cov ^(-1)s stee r / (s_steer^HR cov ^(-1)s steer ), where R cov is the 8×8 receiver covariance matrix, s steer The desired signal steering vector forms a main lobe in the desired signal direction and a null in the interference direction, effectively suppressing multipath interference.

[0352] Time-domain equalization uses a 32nd-order FIR adaptive equalizer, whose coefficients are updated using the LMS algorithm: w(n+1) = w(n) + μe(n)x(n), where μ is the step size factor of 0.01, e(n) is the error signal, and x(n) is the input signal vector. The equalizer compensates for intersymbol interference caused by multipath, improving signal quality. The step size factor is adaptively adjusted based on convergence speed and steady-state error requirements.

[0353] Compensation effect is evaluated in real time by the signal-to-interference-and-noise ratio improvement SINR imp = 10log10(P after ×N before / P before ×N after) and tracking error reduction rate ER track = (σ before - σ after ) / σ before Calculation. The target values ​​are SINR imp ≥6dB and ER track ≥0.4. When the compensation effect is lower than the target value, the system automatically adjusts the algorithm parameters or switches the compensation strategy.

[0354] Example 2: Multi-radar cooperative anti-multipath system

[0355] In the complex electromagnetic environment of large airports, a single radar has limited multipath suppression capabilities. This embodiment uses a coordinated multi-radar configuration with one primary and two secondary radars. The primary radar is located 2,000 meters from the runway centerline extension, and the two secondary radars are located 300 and 500 meters on either side of the runway, forming a baseline angle of approximately 60°.

[0356] The inter-radar spacing is determined by the required resolution. The baseline length, B, is ≥ ρ × R × λ / (2h), where ρ is the required resolution (0.1°), R is the target range, λ is the wavelength (0.033m), and h is the target altitude. For a target at an altitude of 300 meters and a distance of 10 kilometers, the minimum baseline length is approximately 55 meters. The actual spacing of 300-500 meters provides sufficient spatial diversity gain.

[0357] Data fusion uses a weighted least squares method, with weight wi = 1 / σi², where σi is the standard deviation of the measurement error of the i-th radar. The primary radar's angular measurement accuracy is 0.05°, and the auxiliary radar's is 0.1°, corresponding to a weight ratio of 4:1. The fused estimate x̂ = Σ(wixi) / Σwi, with a covariance P = 1 / Σwi. After multi-radar fusion, angular measurement accuracy is improved to 0.03°, meeting the requirements of CAT-III precision approach.

[0358] The time-division multiplexing mechanism ensures that each radar's transmission slot is staggered by Δt = 2R_max / c + 10μs, where R_max is the maximum range of 20 kilometers, the speed of light c = 3 × 10^8 m / s, and the guard time is 10μs. The pulse repetition frequency is 400Hz, with each radar allocated 1 / 3 of the time slot, effectively preventing mutual interference. Frequency-division multiplexing uses a frequency spacing of Δf ≥ 2 / T_pulse, a pulse width of T_pulse = 1μs, and a frequency spacing of at least 2MHz.

[0359] The dominant radar switching is based on a quality factor (Q) = SNR / (σθ × Mp), where SNR is the signal-to-noise ratio, σθ is the angle measurement error, and Mp is the multipath strength. The radar with the higher quality factor assumes the leading role. Switching is triggered when the quality factor of any radar is at least 50% higher than that of the current dominant radar. The switching process is completed within 100ms to ensure tracking continuity.

[0360] The synergy gain is measured using the multi-radar positioning accuracy improvement factor G = √N × cos(Δθ / 2), where N is the number of radars and Δθ is the angle between them. The theoretical gain for a three-radar system configured at a 60° angle is approximately 2.6 times. In actual testing, tracking accuracy in multipath environments increased by 2.2 times, significantly improving system performance.

[0361] Example 3: False Target Identification Based on Target Scattering Characteristics

[0362] A comprehensive RCS database for the Boeing 737-800 has been established to identify multipath false targets. Data collection covers 360° in azimuth and -10° to 30° in elevation, with 1° increments, and frequencies from 8.8 to 9.4 GHz. It includes HH, VV, HV, and VH polarizations. The database includes scattering characteristics for 12 different configurations, including clean configuration, landing gear extended, and various flap positions.

[0363] Real-time RCS measurement uses the single pulse amplitude ratio method to calculate the target angle by the sum and difference beam ratio, combined with the radar equation σ = (4π)³R 4 The scattering cross-section is calculated using the formula Pr / (PtGt²λ²), where Pt is the transmitted power, Gt is the antenna gain, Pr is the received power, and R is the target range. Multi-pulse accumulation improves measurement accuracy to ±1dB, and atmospheric attenuation is corrected using the ITU-R model.

[0364] RCS model matching determines the target aircraft type and configuration based on ADS-B information and extracts the corresponding theoretical RCS value from a database. Taking into account the target's current attitude angle, the expected RCS value σe is calculated through interpolation. The attitude compensation formula σe = σmodel(θ,φ) × cos(α), where α is the pitch attitude deviation angle, which corrects for the impact of flight attitude on RCS.

[0365] Scattering anomaly detection defines an anomaly index (AI) as |σm-σe| / σe, with a three-level judgment: AI < 0.2 for a normal target, 0.2 ≤ AI ≤ 0.4 for a suspicious target, and AI > 0.4 for an abnormal target. In normal flight, the RCS of a Boeing 737 nose is approximately 100 m², the tail is approximately 50 m², and the side is approximately 200 m². When affected by multipath, the RCS can fluctuate rapidly by more than ±30%.

[0366] Polarization analysis measures both horizontal and vertical polarization RCS and calculates the polarization ratio (PR) = σVV / σHH. Under normal circumstances, the polarization ratio of large passenger aircraft is between 0.1 and 3.5, but abnormal values ​​may occur when affected by multipath. The temporal stability of the polarization ratio is also a key indicator. For normal targets, the polarization ratio change rate is less than 10% per second.

[0367] Angular glint detection is achieved by analyzing the statistical characteristics of the RCS time series. The standard deviation σr and mean μr of the RCS within a 10-second window are calculated, and the angular glint index (AS) is defined as σr / μr. The AS for a normal target is <0.3, while the AS for multipath-affected targets is >0.6. Combined with RCS variation frequency analysis, the frequency of RCS glint caused by multipath is generally correlated with the target's motion period.

[0368] The comprehensive feature evaluation combines the four detection results in a weighted manner, with the weights determined based on a large amount of field-measured data. In complex multipath environments, this method achieves a 95% accuracy rate for false target recognition, keeping the false positive rate below 2%, effectively improving the reliability of the tracking system.

[0369] During actual operation at Beijing Capital International Airport, the system was tested on 50 Boeing 737 approaches, successfully identifying and eliminating 86% of multipath false targets. Tracking accuracy was improved from 0.15° with traditional methods to 0.08°, meeting ICAO CAT-III precision approach standards. The entire system's response time was less than 200ms, fully meeting real-time processing requirements.

[0370] like Figure 3 The figure shows a performance comparison between the proposed method and traditional methods. In terms of tracking accuracy improvement, the traditional method achieves approximately 15%, while the proposed method achieves 45%. In terms of multipath suppression, the traditional method achieves approximately 8dB, while the proposed method achieves 18dB. In terms of false target reduction, the traditional method achieves approximately 25%, while the proposed method achieves 65%. All performance indicators have been significantly improved.

[0371] The above-described specific embodiments merely describe preferred embodiments of the present invention and do not limit the scope of protection of the present invention. Any modifications, substitutions, and improvements made to the technical solution of the present invention by a person skilled in the art based on the textual description and drawings provided herein, without departing from the design concept and spirit of the present invention, shall fall within the scope of protection of the present invention. The scope of protection of the present invention is determined by the claims.

Claims

1. A method for reducing the multipath effect of take-off and landing guidance radar based on adaptive off-axis tracking, characterized in that: The following steps are involved: Step S1: The takeoff and landing guidance radar transmits a multi-frequency interrogation signal to the airborne transponder. After receiving the interrogation signal, the airborne transponder transmits a response signal in the direction of the radar. Step S2: The radar simultaneously receives the direct signal and the multipath signal generated by the reflection of the ground or obstacles, separates the direct signal and the multipath signal through multi-dimensional signal feature extraction technology, and establishes a temporal and spatial feature database of the multipath signal; Step S3: Based on the machine learning algorithm, the evolution trend of the multipath effect is predicted in real time. When the impact of the predicted multipath signal on the angular error exceeds the dynamic threshold, the adaptive off-axis tracking mode is started in advance. Step S4: In the off-axis tracking mode, the optimal off-axis angle is dynamically calculated based on the target height, distance, descent speed, and environmental multipath characteristics, and the antenna elevation angle is locked at a fixed angle while continuing the closed-loop tracking of the azimuth. The dynamic calculation of the optimal off-axis angle includes the following implementation steps: Step 4.1: Geometric relationship establishment, based on radar height h r Target height h t and horizontal distance d, establish a three-dimensional geometric model of radar-target-ground, calculate the direct angle and reflection angle, determine the mirror target position, and provide a geometric basis for subsequent optimization; Step 4.2: Calculate the reflection coefficient. Based on the ground material type and electromagnetic properties, use the Fresnel formula to calculate the reflection coefficient at different incident angles, taking into account the effects of ground humidity and roughness on the reflection characteristics. Step 4.3: Design the optimal angle objective function and establish the comprehensive optimization objective function F opt (θ x )=w1·G mp (θ x )+w2·G track (θ x ), balancing the multipath suppression effect and tracking performance loss, where: F opt (θ x ): Angle θ x Comprehensive optimization function under θ x : candidate off-axis angle, w1: multipath suppression weight, value is 0.7 w2: tracking performance weight, value 0.3 G mp (θ x ): Multipath suppression gain function G track (θ x ): Tracking performance function; Step 4.4: Numerical optimization solution is performed. The golden section method is used to solve the optimal off-axis angle in the search interval [0°, 2°]. The convergence accuracy is set to 0.1° and the maximum number of iterations is 100 to ensure the convergence and real-time performance of the algorithm. Step 4.5: Dynamic constraint control, set the angular velocity constraint |dθ / dt|≤ω max and the angular range constraint θ∈[θ min ,θ max ], where ω max is the maximum angular velocity limit, which is 0.5° / s, θ min The minimum off-axis angle is 0°, θ max The maximum off-axis angle is 1.8°; Step 4.6: Smoothing filtering: Use a 3rd-order Butterworth low-pass filter to smooth the angle data. Set the cutoff frequency to 0.1 Hz to prevent antenna system oscillation and ensure the stability of angle changes. Step 4.7: Adaptive parameter adjustment, real-time monitoring of environmental changes, when the environmental mutation index ECI = |Mp cur -Mp pred | / σ pred >Th env , triggers a rapid recalculation of parameters, where: ECI: Environmental Change Index Mp cur : The currently measured multipath strength Mp pred : Predicted multipath strength σ pred : Standard deviation of prediction error Th env : Environmental change threshold, value is 2.5; Step S5: Establish a multipath signal false target recognition model, and through time domain-frequency domain-spatial domain joint analysis, identify and eliminate multipath false targets in real time, retaining the real target information; Step S6: Adopting an angle error estimation method that integrates adaptive Kalman filtering and deep learning to intelligently suppress the angle random error caused by multipath and achieve predictive tracking of the target motion trajectory; Step S7: When it is detected that the target has entered the critical landing phase, the multipath effect compensation mode is started. By building a real-time multipath propagation model, the phase and amplitude of the received signal are compensated to improve the tracking accuracy.

2. The method for reducing the multipath effect of take-off and landing guidance radar based on adaptive off-axis tracking according to claim 1 is characterized in that: The multi-dimensional signal feature extraction technology includes: Step 2.1: Time domain feature extraction: Perform high-speed sampling on the received direct and multipath signals. Calculate the time delay difference between the multipath and direct signals using a cross-correlation algorithm. Extract the signal envelope using a Hilbert transform, calculate the pulse width change rate, and analyze the signal temporal correlation using a sliding window technique. Step 2.2: Frequency domain feature extraction: Use N1-point FFT transform to perform spectrum analysis, extract characteristic parameters, calculate power spectrum density, and analyze spectrum broadening characteristics, where N1 is the number of FFT transform points and is 1024; Step 2.3: Spatial feature extraction: Based on the N2-element uniform linear array, a spatial covariance matrix is ​​constructed. The signal and noise subspaces are obtained through eigenvalue decomposition. The MUSIC algorithm is used for high-precision arrival angle estimation. The root MUSIC algorithm and parabolic interpolation are combined to improve the angle estimation accuracy. Where N2 is the number of antenna elements, which is 8. Step 2.4: Polarization feature extraction: measure the horizontal H and vertical V polarization components simultaneously, calculate the complex polarization ratio, extract the polarization ellipticity and polarization angle characteristic parameters, and analyze the polarization state change; Step 2.5: Feature vector construction, the extracted multi-dimensional features are combined into a 6-dimensional feature vector The feature vector is reduced to 4 dimensions through principal component analysis, retaining 95% of the variance information to form the final multipath feature descriptor, where: Δt: multipath delay difference, ΔT: Pulse width variation, T0: standard pulse width, fd: Doppler shift, θ: signal arrival angle, Azimuth, ε: polarization ellipticity.

3. The method for reducing the multipath effect of take-off and landing guidance radar based on adaptive off-axis tracking according to claim 1, characterized in that: The multipath effect prediction based on machine learning includes the following detailed steps: Step 3.1: Data collection and preprocessing: Establish a long-term data collection mechanism to collect multipath characteristic data under different environmental conditions, perform data cleaning and remove outliers, normalize the input data, and divide the training set, validation set, and test set into a ratio of 7:2:

1. Step 3.2: Data augmentation is performed by adding Gaussian white noise with a signal-to-noise ratio (SNR1) of 20 dB. Random jitter is performed in the time dimension, and new samples are generated by linear interpolation between adjacent samples to expand the training dataset. SNR1 is the baseline signal-to-noise ratio for data augmentation. Step 3.3: Deep neural network construction, design a three-layer fully connected network architecture, with N3 nodes in the input layer, N4 nodes in the first hidden layer, N5 nodes in the second hidden layer, and N6 nodes in the output layer. Add batch normalization and dropout layers to each layer, and set the dropout probability p1, where: N3: Number of input layer nodes, value is 64 N4: The number of nodes in the first hidden layer, the value is 128 N5: The number of nodes in the second hidden layer, the value is 64 N6: The number of output layer nodes, the value is 3, corresponding to Mp, Δt three prediction targets p1: dropout probability, value 0.3 Mp: multipath strength, dimensionless Multipath phase difference, unit rad Δt: multipath delay difference, unit is s; Step 3.4: Design an LSTM temporal network. Build a long short-term memory network to learn the temporal variation of the multipath effect. Set the input sequence length to 10 time steps, the hidden layer to 50 units, and integrate the attention mechanism to identify key moments to achieve temporal modeling of the multipath effect. Step 3.5: Model training and optimization, using the improved loss function L = MSE + λ1∑wi 2 , use Adam optimizer for model training, set early stopping mechanism to prevent overfitting, and use gradient clipping to prevent gradient explosion, where λ1 is the L2 regularization coefficient, with a value of 0.001, and wi is the network weight parameter; Step 3.6: Multi-model fusion prediction, weighted fusion of DNN and LSTM network outputs, the prediction formula is Mp pred (t+k)=α1·DNN out +α2·LSTM out , to achieve forward-looking prediction of multipath strength, where: Mp pred (t+k): multipath strength predicted in k steps k: prediction step length, ranging from 3 to 5 scan cycles α1: DNN network weight, value is 0.6 α2: LSTM network weight, value is 0.4 DNN out : Deep neural network output LSTM out : LSTM network output; Step 3.7: Dynamic threshold calculation: Calculate the dynamic trigger threshold based on historical statistical data and current change trends. The threshold formula is: Implement an adaptive early warning mechanism, including: Th dyn (t): dynamic threshold at time t μ hist : Historical multipath intensity average σ hist : Historical multipath intensity standard deviation k1: statistical weight coefficient, value is 2.5 k2: Change rate weight coefficient, value is 0.15 Multipath intensity change rate.

4. The method for reducing the multipath effect of take-off and landing guidance radar based on adaptive off-axis tracking according to claim 1, characterized in that: The multipath false target recognition model includes the following processing steps: Step 5.1: Coherence detection and analysis: calculate the coherence time and coherence bandwidth of the received signal, analyze the signal correlation characteristics through the cross-correlation function, calculate the coherence coefficient, and mark it as a suspicious target when the coherence coefficient is lower than the set threshold; Step 5.2: Trajectory consistency verification: Build a four-dimensional state space Kalman filter that includes target position and velocity information. Analyze trajectory consistency through innovation test. When the innovation covariance exceeds the statistical threshold, mark it as a trajectory anomaly. Step 5.3: Multi-frame data association: Set a time window for multi-frame data association analysis, calculate the probability of the target's presence between consecutive frames, analyze the continuity and consistency of the target's motion, and eliminate intermittent false targets; Step 5.4: Multi-dimensional confidence fusion, weighted fusion of the results of the four detection methods, the fusion formula is C total =w1·C coh +w2·C traj +w3·C rcs +w4·C prob , establish a comprehensive sentencing mechanism, which includes: C total : Comprehensive confidence, value range [0,1] C coh : Coherence confidence C traj : Trajectory consistency confidence C rcs : RCS characteristic confidence C prob : Existence probability confidence w1, w2, w3, w4: fusion weights, 0.3, 0.3, 0.2, 0.2 respectively; Step 5.5: Adaptive threshold adjustment: dynamically adjust the decision threshold according to the multipath strength and signal-to-noise ratio level of the current environment. The threshold calculation formula is Th adapt =Th base +k3·Mp level +k4·SNR factor ,in: Th adapt : Adaptive decision threshold Th base : Basic threshold, value is 0.75 Mp level : Current multipath strength level SNR factor : Signal-to-noise ratio impact factor k3: multipath strength adjustment coefficient, value is -0.1 k4: Signal-to-noise ratio adjustment coefficient, set to 0.

05.

5. The method for reducing the multipath effect of take-off and landing guidance radar based on adaptive off-axis tracking according to claim 1, characterized in that: The adaptive Kalman filter and deep learning fusion method includes the following implementation steps: Step 6.1: Improve the state equation design and introduce the multipath error compensation term based on the traditional Kalman filter state equation. The state equation is X(k x +1)=[I+ΔTs·A+Δm comp (k x )]X(k x )+ΓU(k x )+W(k x ),in: X(k x ): state vector at time kx, including position and velocity information; I: identity matrix; ΔT s : Sampling interval, value is 0.1s; A: system state transfer matrix; Δm comp (k x ): Multipath error compensation matrix, estimated in real time by neural network; Γ: control input matrix; U(k x ): control input vector; W(k x ): process noise vector; Step 6.2: Neural network noise estimation: Two independent three-layer neural networks are designed to estimate the process noise and observation noise covariance matrices respectively. The network inputs include multipath intensity, signal-to-noise ratio, and target motion parameters to achieve adaptive modeling of noise characteristics. Step 6.3: Reinforcement learning gain optimization: Use the Q-learning algorithm to optimize the Kalman gain parameters. The state space includes multipath strength, signal-to-noise ratio, and prediction error. The action space is the gain adjustment. The reward function guides the parameter optimization direction. Step 6.4: Multi-model structure is established. Three motion models of cruising, acceleration and turning are established. The probability of each model is calculated by the likelihood function. The model probability update formula is μ i (k y )=L i (k y )μ i (k y -1) / ∑j L j (k y )μ j (k y -1), where: μ i (k y ): The i-th model in k y Probability of moment L i (k y ): likelihood function of the i-th model μ i (k y -1): The i-th model is in k y -1 moment probability; Step 6.5: Adaptive parameter adjustment, dynamically adjust the learning rate and forgetting factor according to the stability of the environment. The learning rate formula is α lr (k z )=α0 / (1+β·k z ), where α0 is the initial learning rate with a value of 0.01, β is the decay coefficient with a value of 0.001, and k z is the number of iterations; Step 6.6: Filter fusion output, fuse the multi-model filtering results according to probability weighting, and output the final state estimation and covariance to achieve accurate tracking of target motion in multipath environment.

6. The method for reducing multipath effect of take-off and landing guidance radar based on adaptive off-axis tracking according to claim 1, characterized in that: The multipath effect compensation mode includes the following technical steps: Step 7.1: 3D environment modeling: Integrate terrain data, building information, and material properties to create a 3D environment model with a grid resolution of 5m×5m. Step 7.2: Ray tracing calculation, using the geometric optics approximation method, calculates the multipath propagation path of the electromagnetic wave, considering up to three reflections, and calculates the reflection and transmission coefficients of each interface according to the Fresnel formula; Step 7.3: Adaptive beamforming, calculate the optimal weight vector based on the desired signal direction and interference distribution Multipath interference is suppressed in the spatial domain, where: w beam : beamforming weight vector R cov : Received signal covariance matrix s steer : expected signal steering vector; Step 7.4: Time domain equalization processing uses a 32-order FIR adaptive equalizer and updates the filter coefficients in real time through the LMS algorithm to compensate for inter-symbol interference caused by multipath and improve signal quality. Step 7.5: Compensation effect evaluation: calculate the signal-to-interference-noise ratio improvement and tracking error reduction rate in real time. The evaluation formula is: Signal-to-Interference-Noise Ratio Improvement Evaluation Tracking error reduction rate evaluation where: SINR imp : Signal-to-interference-and-noise ratio improvement, unit: dB, target value ≥ 6dB; P after ,P before : Signal power before and after compensation; N after ,N before : Noise power before and after compensation; ER track : Tracking error reduction rate, target value ≥ 0.4; σ before ,σ after : standard deviation of tracking error before and after compensation; Step 7.6: Dynamic parameter adjustment: adjust the algorithm parameters in real time according to the compensation effect. When the compensation effect is lower than expected, automatically switch the compensation strategy or adjust the parameter settings.

7. The method for reducing multipath effect of take-off and landing guidance radar based on adaptive off-axis tracking according to claim 1, characterized in that: The method also includes an environment adaptive learning mechanism, including the following technical steps: Step 8.1: Construct an airport environmental database by integrating multi-source data to establish a comprehensive environmental database, including electromagnetic characteristic parameters of materials; Step 8.2: Model the material reflection characteristics and establish a database of complex dielectric constants of different ground materials, including the material reflection coefficient; Step 8.3: Pre-calculate the multipath distribution. For each runway direction of the airport, pre-calculate the multipath intensity distribution within the 450° azimuth × 40° elevation grid. Use 2D lookup table format for storage and establish a fast query mechanism; Step 8.4: Seasonal data update: Establish a hierarchical dynamic update strategy, with static data updated annually, semi-static data updated quarterly, and dynamic data updated in real time to ensure the accuracy of the environmental model; Step 8.5: Adaptive modeling of environmental parameters to establish a model of the impact of environmental parameters on multipath effects, including: Temperature affects the refractive index: Humidity affects reflection coefficient: ρ h (H) = ρ dry +0.1×(H / 100); Wind speed affects scattering characteristics: σ s =σ0(1+0.02V)where: n: atmospheric refractive index, P: atmospheric pressure, T: absolute temperature, e: water vapor pressure, ρ h (H): humidity-related reflectance; ρ dry : dry condition reflection coefficient; H: relative humidity, σ s : scattering cross-sectional area, σ0: reference scattering cross-sectional area, V: wind speed; Step 8.6: Model parameter online optimization, using the least squares method to update the environmental model parameters in real time, the objective function J = Σ(y real -y model ) 2 , set the parameter change constraint |Δp|≤0.1p, where: J: optimization objective function; y real : actual observed value; y model : model predicted value; Δp: parameter change; p: model parameter; Convergence criterion: or the number of iterations > 1000; Step 8.7: Abnormal event detection and response, establish an environmental anomaly monitoring mechanism, and define the environmental anomaly index EAI = |M cur -M hist | / σ hist When EAI>3, the abnormal response mode is triggered, where: EAI: Environmental Anomaly Index; M cur : Current multipath strength measurement value; M hist : historical multipath intensity mean; σ hist : Standard deviation of historical data; Step 8.8: Rapid response and recovery: Develop a rapid response mechanism for abnormal situations, requiring abnormal detection response time to be less than 5 seconds, parameter adjustment time to be less than 30 seconds, and system recovery time to be less than 30 seconds; Step 8.9: Adaptive learning optimization: Establish a long-term learning mechanism to continuously optimize the environmental model and prediction algorithm through accumulated observation data, improve the system's adaptability to environmental changes and prediction accuracy, and achieve continuous improvement of system performance.

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